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Mathematics
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New Advances in Mathematical Analysis and Functional Analysis
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New Advances in Mathematical Analysis and Functional Analysis

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 12959

Special Issue Editor

Prof. Dr. Talat Nazir

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
Interests: functional analysis; fixed-point theory and applications; optimization theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to contribute a manuscript to this Special Issue on “New Advances in Mathematical Analysis and Functional Analysis”.

Mathematical analysis and functional analysis plays an important role in many research areas of pure and applied mathematics and is essential for the theory of partial differential equations, numerical analysis, probability theory, optimization theory, and theoretical physics. The impetus came from applications: problems related to ordinary and partial differential equations, numerical analysis, calculus of variations, approximation theory, integral equations, optimization theory, and so on.

The aim of this Special Issue is to gather and publish new results on mathematical analysis, functional analysis, and their applications. We welcome papers on topics including, but not limited to, the following:

  1. Functional analysis;
  2. Mathematical analysis;
  3. Optimization theory;
  4. Control theory;
  5. Variational analysis;
  6. Dynamical system;
  7. Fixed point theory and its application;
  8. Iterated function system;
  9. Fractal theory;
  10. Convex analysis;
  11. Numerical analysis.

Dr. Talat Nazir
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • ordinary and partial differential equations
  • numerical analysis
  • optimization theory
  • calculus of variations
  • approximation theory
  • integral equations
  • fixed point theory and its applications
  • variational analysis
  • dynamical system
  • iterated function system
  • fractal theory
  • convex analysis
  • iteration processes

 

Published Papers (11 papers)

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Research

20 pages, 315 KiB  
Article
Application of Fixed Point Result in Complex Valued Extended b-Metric Space
by Amnah Essa Shammaky and Jamshaid Ahmad
Mathematics 2023, 11(24), 4875; https://doi.org/10.3390/math11244875 - 5 Dec 2023
Viewed by 573
Abstract
The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions [...] Read more.
The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
25 pages, 352 KiB  
Article
Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations
by Hind Alamri, Nawab Hussain and Ishak Altun
Mathematics 2023, 11(23), 4832; https://doi.org/10.3390/math11234832 - 30 Nov 2023
Cited by 1 | Viewed by 586
Abstract
This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for [...] Read more.
This article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
13 pages, 298 KiB  
Article
Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces
by Basit Ali, Hammad Ali, Talat Nazir and Zakaria Ali
Mathematics 2023, 11(21), 4445; https://doi.org/10.3390/math11214445 - 26 Oct 2023
Cited by 1 | Viewed by 789
Abstract
In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ [...] Read more.
In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
11 pages, 290 KiB  
Article
An Extension of Strict Almost Contractions Employing Control Function and Binary Relation with Applications to Boundary Value Problems
by Doaa Filali, Mohammad Akram and Mohammad Dilshad
Mathematics 2023, 11(19), 4027; https://doi.org/10.3390/math11194027 - 22 Sep 2023
Viewed by 595
Abstract
This article comprises some fixed point results for Boyd–Wong-type strict almost contractions using locally L-transitive binary relations. We provide several examples to illustrate our findings. On applying our results, we determine a unique solution of a special boundary value problem. [...] Read more.
This article comprises some fixed point results for Boyd–Wong-type strict almost contractions using locally L-transitive binary relations. We provide several examples to illustrate our findings. On applying our results, we determine a unique solution of a special boundary value problem. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
16 pages, 305 KiB  
Article
Generalized Iterated Function Systems on b-Metric Spaces
by Izabella Abraham and Radu Miculescu
Mathematics 2023, 11(13), 2826; https://doi.org/10.3390/math11132826 - 23 Jun 2023
Cited by 1 | Viewed by 1069
Abstract
An iterated function system consists of a complete metric space (X,d) and a finite family of contractions f1,⋯,fn:X→X. A generalized iterated function system comprises a finite family of [...] Read more.
An iterated function system consists of a complete metric space (X,d) and a finite family of contractions f1,⋯,fn:X→X. A generalized iterated function system comprises a finite family of contractions defined on the Cartesian product Xm with values in X. In this paper, we want to investigate generalized iterated function systems in the more general setting of b-metric spaces. We prove that such a system admits a unique attractor and, under some further restrictions on the b-metric, it depends continuously on parameters. We also provide two examples of generalized iterated function systems defined on a particular b-metric space and find the corresponding attractors. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
19 pages, 347 KiB  
Article
Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation
by N. Seshagiri Rao, Zoran D. Mitrović, Dania Santina and Nabil Mlaiki
Mathematics 2023, 11(11), 2580; https://doi.org/10.3390/math11112580 - 5 Jun 2023
Cited by 1 | Viewed by 1038
Abstract
In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. [...] Read more.
In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
30 pages, 368 KiB  
Article
Fuzzy Triple Controlled Metric like Spaces with Applications
by Naeem Saleem, Salman Furqan, Kinda Abuasbeh and Muath Awadalla
Mathematics 2023, 11(6), 1390; https://doi.org/10.3390/math11061390 - 13 Mar 2023
Viewed by 1196
Abstract
In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy [...] Read more.
In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy b–rectangular and fuzzy rectangular metric like spaces. Various examples are given to justify our definitions and results. As for the topological aspect, we prove a fuzzy triple controlled metric like space is not Hausdorff. We also apply our main result to solve the uniqueness of the solution of a fractional differential equation. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
17 pages, 844 KiB  
Article
Compartmental Unpredictable Functions
by Marat Akhmet, Madina Tleubergenova and Akylbek Zhamanshin
Mathematics 2023, 11(5), 1069; https://doi.org/10.3390/math11051069 - 21 Feb 2023
Cited by 4 | Viewed by 1300
Abstract
There is a huge family of recurrent functions, which starts with equilibria and ends with Poisson stable functions. They are fundamental in theoretical and application senses, and they admit a famous history. Recently, we have added the unpredictable functions to the family. The [...] Read more.
There is a huge family of recurrent functions, which starts with equilibria and ends with Poisson stable functions. They are fundamental in theoretical and application senses, and they admit a famous history. Recently, we have added the unpredictable functions to the family. The research has been performed in several papers and books. Obviously, theoretical and application merits of functions increase if one provides rigorously approved efficient methods of construction of concrete examples, as well as their numerical simulations. In the present study, we met the challenges for unpredictability by considering functions of two variables on diagonals. Algorithms have been created, and they are both deterministic and random. Characteristics are introduced to evaluate contributions of periodic and unpredictable components to the dynamics, and they are clearly illustrated in graphs of the functions. Definitions of non-periodic compartmental functions are provided as suggestions for the research in the future. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
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18 pages, 346 KiB  
Article
Integral Equation via Fixed Point Theorems on a New Type of Convex Contraction in b-Metric and 2-Metric Spaces
by Gunasekaran Nallaselli, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Zoran D. Mitrović, Ahmad Aloqaily and Nabil Mlaiki
Mathematics 2023, 11(2), 344; https://doi.org/10.3390/math11020344 - 9 Jan 2023
Cited by 3 | Viewed by 1601
Abstract
Our paper is devoted to describing a new way of generalized convex contraction of type-2 in the framework of b-metric spaces and 2-metric spaces. First, the concept of a new generalized convex contraction on b-metric spaces and 2-metric spaces is introduced, [...] Read more.
Our paper is devoted to describing a new way of generalized convex contraction of type-2 in the framework of b-metric spaces and 2-metric spaces. First, the concept of a new generalized convex contraction on b-metric spaces and 2-metric spaces is introduced, and fixed point theorem is extended to these spaces. Some examples supporting our main results are also presented. Finally, we apply our main result to approximating the solution of the Fredholm integral equation. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
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17 pages, 323 KiB  
Article
Solution of Integral Equations Using Some Multiple Fixed Point Results in Special Kinds of Distance Spaces
by Maliha Rashid, Naeem Saleem, Rabia Bibi and Reny George
Mathematics 2022, 10(24), 4707; https://doi.org/10.3390/math10244707 - 11 Dec 2022
Cited by 5 | Viewed by 969
Abstract
In this paper, we explore some extensions of multiple fixed point results for various distance spaces such as s-distance space, s,q-distance space, and balanced distance space. Some examples are also discussed for the elaboration of these generalized structures. An [...] Read more.
In this paper, we explore some extensions of multiple fixed point results for various distance spaces such as s-distance space, s,q-distance space, and balanced distance space. Some examples are also discussed for the elaboration of these generalized structures. An application of our result that demonstrates the existence of a unique solution of a system of integral equations is also provided. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
9 pages, 275 KiB  
Article
New Applications of Perov’s Fixed Point Theorem
by Sorin Mureşan, Loredana Florentina Iambor and Omar Bazighifan
Mathematics 2022, 10(23), 4597; https://doi.org/10.3390/math10234597 - 4 Dec 2022
Cited by 3 | Viewed by 1142
Abstract
The goal of this paper is to consider a differential equation system written as an interesting equivalent form that has not been used before. Using Perov’s fixed point theorem in generalized metric spaces, the existence and uniqueness of the solution are obtained for [...] Read more.
The goal of this paper is to consider a differential equation system written as an interesting equivalent form that has not been used before. Using Perov’s fixed point theorem in generalized metric spaces, the existence and uniqueness of the solution are obtained for the proposed system. The approximation of the solution is given, and as a novelty, the approximation of its derivative is also obtained using the same iteration steps. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Functional Analysis)
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