Mathematics

20 pages, 291 KiB

Open AccessEditor’s ChoiceArticle

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

by Jiqiang Jiang, Donal O’Regan, Jiafa Xu and Yujun Cui

Mathematics 2019, 7(5), 439; https://doi.org/10.3390/math7050439 - 17 May 2019

Cited by 27 | Viewed by 2730

This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows

(p - 1)

-superlinearly and

(p - 1)

-sublinearly, the existence of positive solutions is obtained via fixed [...] Read more.

This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows

(p - 1)

-superlinearly and

(p - 1)

-sublinearly, the existence of positive solutions is obtained via fixed point index. Moreover, using an increasing operator fixed-point theorem, the uniqueness of positive solutions and uniform convergence sequences are also established. Full article

21 pages, 425 KiB

Open AccessEditor’s ChoiceReview

Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial

by Roberto Garrappa, Eva Kaslik and Marina Popolizio

Mathematics 2019, 7(5), 407; https://doi.org/10.3390/math7050407 - 7 May 2019

Cited by 98 | Viewed by 7430

Abstract

Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly used operators and illustrated two approaches [...] Read more.

Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly used operators and illustrated two approaches to generalize integer-order derivatives to fractional order; the aim was to provide a tool for a full understanding of the specific features of each fractional derivative and to better highlight their differences. We hence provided a guide to the evaluation of fractional integrals and derivatives of some elementary functions and studied the action of different derivatives on the same function. In particular, we observed how Riemann–Liouville and Caputo’s derivatives converge, on long times, to the Grünwald–Letnikov derivative which appears as an ideal generalization of standard integer-order derivatives although not always useful for practical applications. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)

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35 pages, 3547 KiB

Open AccessEditor’s ChoiceArticle

Enhancing Elephant Herding Optimization with Novel Individual Updating Strategies for Large-Scale Optimization Problems

by Jiang Li, Lihong Guo, Yan Li and Chang Liu

Mathematics 2019, 7(5), 395; https://doi.org/10.3390/math7050395 - 30 Apr 2019

Cited by 37 | Viewed by 4442

Abstract

Inspired by the behavior of elephants in nature, elephant herd optimization (EHO) was proposed recently for global optimization. Like most other metaheuristic algorithms, EHO does not use the previous individuals in the later updating process. If the useful information in the previous individuals [...] Read more.

Inspired by the behavior of elephants in nature, elephant herd optimization (EHO) was proposed recently for global optimization. Like most other metaheuristic algorithms, EHO does not use the previous individuals in the later updating process. If the useful information in the previous individuals were fully exploited and used in the later optimization process, the quality of solutions may be improved significantly. In this paper, we propose several new updating strategies for EHO, in which one, two, or three individuals are selected from the previous iterations, and their useful information is incorporated into the updating process. Accordingly, the final individual at this iteration is generated according to the elephant generated by the basic EHO, and the selected previous elephants through a weighted sum. The weights are determined by a random number and the fitness of the elephant individuals at the previous iteration. We incorporated each of the six individual updating strategies individually into the basic EHO, creating six improved variants of EHO. We benchmarked these proposed methods using sixteen test functions. Our experimental results demonstrated that the proposed improved methods significantly outperformed the basic EHO. Full article

(This article belongs to the Special Issue Evolutionary Computation)

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25 pages, 512 KiB

Open AccessEditor’s ChoiceArticle

A Two-Echelon Supply Chain Management With Setup Time and Cost Reduction, Quality Improvement and Variable Production Rate

by Bikash Koli Dey, Biswajit Sarkar and Sarla Pareek

Mathematics 2019, 7(4), 328; https://doi.org/10.3390/math7040328 - 3 Apr 2019

Cited by 39 | Viewed by 5841

Abstract

This model investigates the variable production cost for a production house; under a two-echelon supply chain management where a single vendor and multi-retailers are involved. This production system goes through a long run system and generates an out-of-control state due to different issues [...] Read more.

This model investigates the variable production cost for a production house; under a two-echelon supply chain management where a single vendor and multi-retailers are involved. This production system goes through a long run system and generates an out-of-control state due to different issues and produces defective items. This model considers the reduction of the defective rate and setup cost through investment. A discrete investment for setup cost reduction and a continuous investment is considered to reduce the defective rate and to increase the quality of products. Setup and processing time are dependent on lead time in this model. The model is solved analytically to find the optimal values of the production rate, safety factors, optimum quantity, lead time length, investment for setup cost reduction, and the probability of the production process going out-of-control. An efficient algorithm is constructed to find the optimal solution numerically and sensitivity analysis is given to show the impact of different parameters. A case study and different cases are also given to validate the model. Full article

(This article belongs to the Special Issue Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain)

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10 pages, 273 KiB

Open AccessEditor’s ChoiceArticle

The Bounds of Vertex Padmakar–Ivan Index on k-Trees

by Shaohui Wang, Zehui Shao, Jia-Bao Liu and Bing Wei

Mathematics 2019, 7(4), 324; https://doi.org/10.3390/math7040324 - 1 Apr 2019

Cited by 18 | Viewed by 3021

Abstract

The Padmakar–Ivan (

P I

) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges

u v

of a graph such that these vertices are not equidistant from u [...] Read more.

The Padmakar–Ivan (

P I

) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges

u v

of a graph such that these vertices are not equidistant from u and v. In this paper, we explore the results of

P I

-indices from trees to recursively clustered trees, the k-trees. Exact sharp upper bounds of PI indices on k-trees are obtained by the recursive relationships, and the corresponding extremal graphs are given. In addition, we determine the

P I

-values on some classes of k-trees and compare them, and our results extend and enrich some known conclusions. Full article

(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)

22 pages, 3000 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Multivariate Theory of Connections

by Daniele Mortari and Carl Leake

Mathematics 2019, 7(3), 296; https://doi.org/10.3390/math7030296 - 22 Mar 2019

Cited by 38 | Viewed by 4844

Abstract

This paper extends the univariate Theory of Connections, introduced in (Mortari, 2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface, introduced by (Coons, 1984), by providing analytical expressions, called [...] Read more.

This paper extends the univariate Theory of Connections, introduced in (Mortari, 2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface, introduced by (Coons, 1984), by providing analytical expressions, called constrained expressions, representing all possible surfaces with assigned boundary constraints in terms of functions and arbitrary-order derivatives. In two dimensions, these expressions, which contain a freely chosen function,

g (x, y)

, satisfy all constraints no matter what the

g (x, y)

is. The boundary constraints considered in this article are Dirichlet, Neumann, and any combinations of them. Although the focus of this article is on two-dimensional spaces, the final section introduces the Multivariate Theory of Connections, validated by mathematical proof. This represents the multivariate extension of the Theory of Connections subject to arbitrary-order derivative constraints in rectangular domains. The main task of this paper is to provide an analytical procedure to obtain constrained expressions in any space that can be used to transform constrained problems into unconstrained problems. This theory is proposed mainly to better solve PDE and stochastic differential equations. Full article

(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)

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18 pages, 2526 KiB

Open AccessEditor’s ChoiceArticle

An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation

by Pundikala Veeresha, Doddabhadrappla Gowda Prakasha and Dumitru Baleanu

Mathematics 2019, 7(3), 265; https://doi.org/10.3390/math7030265 - 14 Mar 2019

Cited by 52 | Viewed by 3551

Abstract

The

q

-homotopy analysis transform method (

q

-HATM) is employed to find the solution for the fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with [...] Read more.

The

q

-homotopy analysis transform method (

q

-HATM) is employed to find the solution for the fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology. Full article

(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2019)

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24 pages, 5440 KiB

Open AccessEditor’s ChoiceArticle

Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

by Harendra Singh, Rajesh K. Pandey and Hari Mohan Srivastava

Mathematics 2019, 7(3), 224; https://doi.org/10.3390/math7030224 - 27 Feb 2019

Cited by 43 | Viewed by 3837

Abstract

The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method. The Ritz method has allowed many researchers to [...] Read more.

The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method. The Ritz method has allowed many researchers to solve different forms of fractional variational problems in recent years. The NLFVP is solved by applying the Ritz method using different orthogonal polynomials. Further, the approximate solution is obtained by solving a system of nonlinear algebraic equations. Error and convergence analysis of the discussed method is also provided. Numerical simulations are performed on illustrative examples to test the accuracy and applicability of the method. For comparison purposes, different polynomials such as 1) Shifted Legendre polynomials, 2) Shifted Chebyshev polynomials of the first kind, 3) Shifted Chebyshev polynomials of the third kind, 4) Shifted Chebyshev polynomials of the fourth kind, and 5) Gegenbauer polynomials are considered to perform the numerical investigations in the test examples. Further, the obtained results are presented in the form of tables and figures. The numerical results are also compared with some known methods from the literature. Full article

(This article belongs to the Special Issue Fractional-Order Integral and Derivative Operators and Their Applications)

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17 pages, 307 KiB

Open AccessEditor’s ChoiceArticle

Dynamic Keynesian Model of Economic Growth with Memory and Lag

by Vasily E. Tarasov and Valentina V. Tarasova

Mathematics 2019, 7(2), 178; https://doi.org/10.3390/math7020178 - 15 Feb 2019

Cited by 21 | Viewed by 6116

Abstract

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the [...] Read more.

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)

15 pages, 2766 KiB

Open AccessEditor’s ChoiceArticle

A Partial-Consensus Posterior-Aggregation FAHP Method—Supplier Selection Problem as an Example

by Yu-Cheng Wang and Tin-Chih Toly Chen

Mathematics 2019, 7(2), 179; https://doi.org/10.3390/math7020179 - 15 Feb 2019

Cited by 40 | Viewed by 3278

Abstract

Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this [...] Read more.

Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this problem, a partial-consensus posterior-aggregation FAHP (PCPA-FAHP) approach is proposed in this study. The PCPA-FAHP approach seeks a partial consensus among most DMs instead of an overall consensus among all DMs, thereby increasing the possibility of reaching a consensus. Subsequently, the aggregation result is defuzzified using the prevalent center-of-gravity method. The PCPA-FAHP approach was applied to a supplier selection problem to validate its effectiveness. According to the experimental results, the PCPA-FAHP approach not only successfully found out the partial consensus among the DMs, but also shrunk the widths of the estimated fuzzy weights to enhance the precision of the FAHP analysis. Full article

(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)

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15 pages, 280 KiB

Open AccessEditor’s ChoiceArticle

Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

by Hari M. Srivastava, Qazi Zahoor Ahmad, Nasir Khan, Nazar Khan and Bilal Khan

Mathematics 2019, 7(2), 181; https://doi.org/10.3390/math7020181 - 15 Feb 2019

Cited by 111 | Viewed by 3909

Abstract

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk

U

. In particular, we find the Hankel [...] Read more.

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk

U

. In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results. Full article

(This article belongs to the Special Issue Fractional-Order Integral and Derivative Operators and Their Applications)

14 pages, 254 KiB

Open AccessEditor’s ChoiceArticle

New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex

by Seth Kermausuor, Eze R. Nwaeze and Ana M. Tameru

Mathematics 2019, 7(2), 183; https://doi.org/10.3390/math7020183 - 15 Feb 2019

Cited by 17 | Viewed by 2963

Abstract

In this paper, we introduced some new integral inequalities of the Hermite–Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly

η

-convex functions via the Katugampola fractional integrals. Full article

(This article belongs to the Special Issue Inequalities)

26 pages, 747 KiB

Open AccessEditor’s ChoiceArticle

Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

by Feng Feng, Meiqi Liang, Hamido Fujita, Ronald R. Yager and Xiaoyan Liu

Mathematics 2019, 7(2), 166; https://doi.org/10.3390/math7020166 - 13 Feb 2019

Cited by 46 | Viewed by 3081

Abstract

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a [...] Read more.

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems. Full article

(This article belongs to the Section Engineering Mathematics)

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35 pages, 924 KiB

Open AccessEditor’s ChoiceArticle

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

by A. M. Elaiw and E. Kh. Elnahary

Mathematics 2019, 7(2), 157; https://doi.org/10.3390/math7020157 - 9 Feb 2019

Cited by 52 | Viewed by 2789

Abstract

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4

^{+}

T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. [...] Read more.

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4

^{+}

T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles. Full article

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14 pages, 358 KiB

Open AccessEditor’s ChoiceArticle

Fractional Derivatives: The Perspective of System Theory

by Manuel Duarte Ortigueira and José Tenreiro Machado

Mathematics 2019, 7(2), 150; https://doi.org/10.3390/math7020150 - 5 Feb 2019

Cited by 48 | Viewed by 4163

Abstract

This paper addresses the present day problem of multiple proposals for operators under the umbrella of “fractional derivatives”. Several papers demonstrated that various of those “novel” definitions are incorrect. Here the classical system theory is applied to develop a unified framework to clarify [...] Read more.

This paper addresses the present day problem of multiple proposals for operators under the umbrella of “fractional derivatives”. Several papers demonstrated that various of those “novel” definitions are incorrect. Here the classical system theory is applied to develop a unified framework to clarify this important topic in Fractional Calculus. Full article

(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)

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5 pages, 250 KiB

Open AccessEditor’s ChoiceArticle

Desiderata for Fractional Derivatives and Integrals

by Rudolf Hilfer and Yuri Luchko

Mathematics 2019, 7(2), 149; https://doi.org/10.3390/math7020149 - 4 Feb 2019

Cited by 94 | Viewed by 5750

Abstract

The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead [...] Read more.

The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria. Full article

(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)

17 pages, 2881 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Novel Bat Algorithm with Multiple Strategies Coupling for Numerical Optimization

by Yechuang Wang, Penghong Wang, Jiangjiang Zhang, Zhihua Cui, Xingjuan Cai, Wensheng Zhang and Jinjun Chen

Mathematics 2019, 7(2), 135; https://doi.org/10.3390/math7020135 - 1 Feb 2019

Cited by 120 | Viewed by 12595

Abstract

A bat algorithm (BA) is a heuristic algorithm that operates by imitating the echolocation behavior of bats to perform global optimization. The BA is widely used in various optimization problems because of its excellent performance. In the bat algorithm, the global search capability [...] Read more.

A bat algorithm (BA) is a heuristic algorithm that operates by imitating the echolocation behavior of bats to perform global optimization. The BA is widely used in various optimization problems because of its excellent performance. In the bat algorithm, the global search capability is determined by the parameter loudness and frequency. However, experiments show that each operator in the algorithm can only improve the performance of the algorithm at a certain time. In this paper, a novel bat algorithm with multiple strategies coupling (mixBA) is proposed to solve this problem. To prove the effectiveness of the algorithm, we compared it with CEC2013 benchmarks test suits. Furthermore, the Wilcoxon and Friedman tests were conducted to distinguish the differences between it and other algorithms. The results prove that the proposed algorithm is significantly superior to others on the majority of benchmark functions. Full article

(This article belongs to the Special Issue Evolutionary Computation)

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6 pages, 746 KiB

Open AccessEditor’s ChoiceArticle

Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network

by Ioannis Dassios, Andrew Keane and Paul Cuffe

Mathematics 2019, 7(1), 106; https://doi.org/10.3390/math7010106 - 20 Jan 2019

Cited by 12 | Viewed by 4519

Abstract

Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These [...] Read more.

Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis. Full article

(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)

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8 pages, 235 KiB

Open AccessEditor’s ChoiceArticle

ω-Interpolative Ćirić-Reich-Rus-Type Contractions

by Hassen Aydi, Erdal Karapinar and Antonio Francisco Roldán López de Hierro

Mathematics 2019, 7(1), 57; https://doi.org/10.3390/math7010057 - 8 Jan 2019

Cited by 104 | Viewed by 3836

Abstract

In this paper, using the concept of

ω

-admissibility, we prove some fixed point results for interpolate Ćirić-Reich-Rus-type contraction mappings. We also present some consequences and a useful example. Full article

(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)

15 pages, 793 KiB

Open AccessEditor’s ChoiceArticle

An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

by Yonghong Yao, Mihai Postolache and Jen-Chih Yao

Mathematics 2019, 7(1), 61; https://doi.org/10.3390/math7010061 - 8 Jan 2019

Cited by 98 | Viewed by 5585

Abstract

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested [...] Read more.

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

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