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Mathematics
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Fixed Point Theory
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Fixed Point Theory

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

Deadline for manuscript submissions: closed (30 April 2018) | Viewed by 29971

Special Issue Editors

Prof. Dr. Shahram Shahram Rezapour

E-Mail Website
Guest Editor
1. Department of Medical Research, China Medical University, Taichung, Taiwan
2. Department of Mathematics, Azerbaijan Shahid Madani University, Tabriz, Iran
Interests: approximation theory; fixed point theory; fractional differential equations; fractional finite difference equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Erdal Karapinar

E-Mail Website
Guest Editor
Department of Mathematics, Atilim University, TR-06836 Ankara, Turkey
Interests: numerical modeling; numerical analysis; mathematical modelling; mathematical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is very well known that Nonlinear Methods have extreme role in modern mathematical applied theories such fractional differentiation equations or inclusions, study anomalous social and physical behaviors, finite difference calculus, systems of delay differential equations, biological and engineering different models. 

This special Issue deals with the theory, especially applications in science, engineering, physical or chemical new models and convergence of distinct iterative methods. We will accept high-quality papers having original research results. 

The purpose of this Special Issue is to bring mathematicians together with physicists, engineers, as well as other scientists, for whom nonlinear methods are valuable research tools.

Prof. Dr. Shahram Rezapour
Prof. Dr. Erdal Karapinar
Guest Editors

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

  • discrete fractional equations
  • finite difference equations
  • fixed point
  • fractional differential equations
  • inclusion
  • integral equations
  • iterative method
  • modelling problems
  • multifunction

Published Papers (9 papers)

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Research

11 pages, 240 KiB  
Article
Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications to Fixed Point Theory
by Wei-Shih Du, Erdal Karapınar and Zhenhua He
Mathematics 2018, 6(7), 117; https://doi.org/10.3390/math6070117 - 09 Jul 2018
Cited by 6 | Viewed by 2956
Abstract
In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The [...] Read more.
In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature. Full article
(This article belongs to the Special Issue Fixed Point Theory)
14 pages, 316 KiB  
Article
Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces
by Eshagh Hashemi and Reza Saadati
Mathematics 2018, 6(6), 93; https://doi.org/10.3390/math6060093 - 05 Jun 2018
Cited by 2 | Viewed by 3237
Abstract
We consider a distance function on generalized metric spaces and we get a generalization of Ekeland Variational Principle (EVP). Next, we prove that EVP is equivalent to Caristi–Kirk fixed point theorem and minimization Takahashi’s theorem. Full article
(This article belongs to the Special Issue Fixed Point Theory)
15 pages, 267 KiB  
Article
Near Fixed Point Theorems in Hyperspaces
by Hsien-Chung Wu
Mathematics 2018, 6(6), 90; https://doi.org/10.3390/math6060090 - 28 May 2018
Cited by 4 | Viewed by 2853
Abstract
The hyperspace consists of all the subsets of a vector space. It is well-known that the hyperspace is not a vector space because it lacks the concept of inverse element. This also says that we cannot consider its normed structure, and some kinds [...] Read more.
The hyperspace consists of all the subsets of a vector space. It is well-known that the hyperspace is not a vector space because it lacks the concept of inverse element. This also says that we cannot consider its normed structure, and some kinds of fixed point theorems cannot be established in this space. In this paper, we shall propose the concept of null set that will be used to endow a norm to the hyperspace. This normed hyperspace is clearly not a conventional normed space. Based on this norm, the concept of Cauchy sequence can be similarly defined. In addition, a Banach hyperspace can be defined according to the concept of Cauchy sequence. The main aim of this paper is to study and establish the so-called near fixed point theorems in Banach hyperspace. Full article
(This article belongs to the Special Issue Fixed Point Theory)
11 pages, 253 KiB  
Article
Non-Unique Fixed Point Results in Extended B-Metric Space
by Badr Alqahtani, Andreea Fulga and Erdal Karapınar
Mathematics 2018, 6(5), 68; https://doi.org/10.3390/math6050068 - 02 May 2018
Cited by 41 | Viewed by 4465
Abstract
In this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results. Full article
(This article belongs to the Special Issue Fixed Point Theory)
8 pages, 236 KiB  
Article
Fixed Point Theorems for Almost Z-Contractions with an Application
by Huseyin Isik, Nurcan Bilgili Gungor, Choonkil Park and Sun Young Jang
Mathematics 2018, 6(3), 37; https://doi.org/10.3390/math6030037 - 07 Mar 2018
Cited by 14 | Viewed by 3907
Abstract
In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results. Full article
(This article belongs to the Special Issue Fixed Point Theory)
15 pages, 274 KiB  
Article
Bi-Additive s-Functional Inequalities and Quasi-∗-Multipliers on Banach Algebras
by Choonkil Park
Mathematics 2018, 6(3), 31; https://doi.org/10.3390/math6030031 - 26 Feb 2018
Cited by 7 | Viewed by 3155
Abstract
Using the fixed point method, we prove the Hyers-Ulam stability of quasi-∗-multipliers on Banach ∗-algebras and unital C*-algebras, associated to bi-additive s-functional inequalities. Full article
(This article belongs to the Special Issue Fixed Point Theory)
21 pages, 273 KiB  
Article
Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces
by Hsien-Chung Wu
Mathematics 2018, 6(2), 29; https://doi.org/10.3390/math6020029 - 23 Feb 2018
Cited by 8 | Viewed by 2363
Abstract
We propose the so-called fuzzy semi-metric space in which the symmetric condition is not assumed to be satisfied. In this case, there are four kinds of triangle inequalities that should be considered. The purpose of this paper is to study the common coincidence [...] Read more.
We propose the so-called fuzzy semi-metric space in which the symmetric condition is not assumed to be satisfied. In this case, there are four kinds of triangle inequalities that should be considered. The purpose of this paper is to study the common coincidence points and common fixed points in the newly proposed fuzzy semi-metric spaces endowed with the so-called ⋈-triangle inequality. The other three different kinds of triangle inequalities will be the future research, since they cannot be similarly investigated as the case of ⋈-triangle inequality. Full article
(This article belongs to the Special Issue Fixed Point Theory)
8 pages, 209 KiB  
Article
On Generalized Pata Type Contractions
by Geno Kadwin Jacob, M. S. Khan, Choonkil Park and Sungsik Yun
Mathematics 2018, 6(2), 25; https://doi.org/10.3390/math6020025 - 13 Feb 2018
Cited by 7 | Viewed by 2852
Abstract
In this paper, the existence of fixed point for Pata type Zamfirescu mapping in a complete metric space is proved. Our result give existence of fixed point for a wider class of functions and also prove the existence of best proximity point to [...] Read more.
In this paper, the existence of fixed point for Pata type Zamfirescu mapping in a complete metric space is proved. Our result give existence of fixed point for a wider class of functions and also prove the existence of best proximity point to the result on “A fixed point theorem in metric spaces”, given by vittorino Pata. Full article
(This article belongs to the Special Issue Fixed Point Theory)
235 KiB  
Article
A Fixed Point Approach to the Stability of a Mean Value Type Functional Equation
by Soon-Mo Jung and Yang-Hi Lee
Mathematics 2017, 5(4), 78; https://doi.org/10.3390/math5040078 - 13 Dec 2017
Cited by 4 | Viewed by 2627
Abstract
We prove the generalized Hyers–Ulam stability of a mean value type functional equation f ( x ) − g ( y ) = ( x − y ) h ( x + y ) by applying a method originated from fixed point theory. [...] Read more.
We prove the generalized Hyers–Ulam stability of a mean value type functional equation f ( x ) − g ( y ) = ( x − y ) h ( x + y ) by applying a method originated from fixed point theory. Full article
(This article belongs to the Special Issue Fixed Point Theory)
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