Recent Advances in Fixed Point Theory and Its Applications

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

Deadline for manuscript submissions: closed (30 June 2019) | Viewed by 33372

Special Issue Editors


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Guest Editor
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Interests: functional analysis; operator theory; linear topological invariants; fixed point theory; best proximity
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Statistics and Operations Research, University of Granada, 18010 Granada, Spain
Interests: fuzzy numbers; fuzzy decision making; fuzzy regression; aggregation functions; fixed point theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to collect and announce the recent advances and improvements in nonlinear analysis, in particular, fixed point theory, which may help to solve and improve the difficulties arising in the analysis and computational simulation of nonlinear, real-world problems. Both the determination of the qualitative features of solutions for nonlinear models and the analysis of numerical methods to approximate these solutions are of special interest. Papers that study the existence and uniqueness of solutions of nonlinear partial differential equations, systems, as well as relevant features of solution spaces are especially welcome. Works that emphasize the rigorous analysis of computational techniques to simulate the dynamics of complex models in the sciences, engineering and economics are solicited for this Special Issue.

This Special Issue not emphasizes particular mathematical models of nonlinear problems, but also the investigation of the analytical features of the solutions to underlying problems and the analysis of approximation techniques to simulate them. Both deterministic and stochastic models arising in science, engineering and economics will be considered, and pertinent applications to the resolution of practical problems are expected.

Prof. Dr. Erdal Karapinar
Prof. Dr. Antonio Francisco Roldan Lopez de Hierro
Guest Editors

Topics for this mini symposium include, but are not limited to:

  • fixed point theory in various abstract spaces
  • existence and uniqueness of coupled/tripled/quadrupled fixed points
  • coincidence point theory
  • existence and uniqueness of common fixed points
  • well-posedness of fixed point results
  • advances in multivalued fixed point theorems
  • fixed point methods for the equilibrium problems and applications
  • iterative methods for the fixed points of the nonexpansive-type mappings
  • picard operators in various abstract spaces
  • applications to different areas

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.

Published Papers (10 papers)

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Research

9 pages, 237 KiB  
Article
Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations
by Anupam Das, Bipan Hazarika and Poom Kumam
Mathematics 2019, 7(3), 214; https://doi.org/10.3390/math7030214 - 26 Feb 2019
Cited by 25 | Viewed by 3330
Abstract
In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also [...] Read more.
In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
11 pages, 272 KiB  
Article
Some Common Fixed Point Theorems in Ordered Partial Metric Spaces via ℱ-Generalized Contractive Type Mappings
by Pooja Dhawan and Jatinderdeep Kaur
Mathematics 2019, 7(2), 193; https://doi.org/10.3390/math7020193 - 18 Feb 2019
Cited by 2 | Viewed by 2832
Abstract
In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results [...] Read more.
In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
10 pages, 268 KiB  
Article
Fisher-Type Fixed Point Results in b-Metric Spaces
by Badr Alqahtani, Andreea Fulga, Erdal Karapınar and Ali Özturk
Mathematics 2019, 7(1), 102; https://doi.org/10.3390/math7010102 - 18 Jan 2019
Cited by 5 | Viewed by 3579
Abstract
In this paper, we prove some common fixed-point theorems for two self-mappings in the context of a complete b-metric space by proposing a new contractive type condition. Further, we derive a result for three self-mappings in the same setting. We provide two [...] Read more.
In this paper, we prove some common fixed-point theorems for two self-mappings in the context of a complete b-metric space by proposing a new contractive type condition. Further, we derive a result for three self-mappings in the same setting. We provide two examples to demonstrate the validity of the obtained results. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
15 pages, 576 KiB  
Article
α H-ψH-Multivalued Contractive Mappings and Related Results in Complete Metric Spaces with an Application
by Pooja Dhawan, Kapil Jain and Jatinderdeep Kaur
Mathematics 2019, 7(1), 68; https://doi.org/10.3390/math7010068 - 09 Jan 2019
Cited by 1 | Viewed by 1958
Abstract
In the present article, the notion of α H- ψ H-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and [...] Read more.
In the present article, the notion of α H- ψ H-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa’s (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
8 pages, 235 KiB  
Article
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 - 08 Jan 2019
Cited by 97 | Viewed by 3365
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)
11 pages, 260 KiB  
Article
Common Fixed Points for Mappings under Contractive Conditions of (α,β,ψ)-Admissibility Type
by Wasfi Shatanawi
Mathematics 2018, 6(11), 261; https://doi.org/10.3390/math6110261 - 18 Nov 2018
Cited by 19 | Viewed by 2486
Abstract
In this paper, we introduce the notion of ( α , β , ψ ) -contraction for a pair of mappings ( S , T ) defined on a set X. We use our new notion to create and prove a common [...] Read more.
In this paper, we introduce the notion of ( α , β , ψ ) -contraction for a pair of mappings ( S , T ) defined on a set X. We use our new notion to create and prove a common fixed point theorem for two mappings defined on a metric space ( X , d ) under a set of conditions. Furthermore, we employ our main result to get another new result. Our results are modifications of many existing results in the literature. An example is included in order to show the authenticity of our main result. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
11 pages, 251 KiB  
Article
On p-Common Best Proximity Point Results for S-Weakly Contraction in Complete Metric Spaces
by Chayut Kongban, Poom Kumam, Somayya Komal and Kanokwan Sitthithakerngkiet
Mathematics 2018, 6(11), 241; https://doi.org/10.3390/math6110241 - 07 Nov 2018
Cited by 2 | Viewed by 2857
Abstract
In this work, we introduced new notions of a new contraction named S -weakly contraction; after that, we obtained the p-common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak [...] Read more.
In this work, we introduced new notions of a new contraction named S -weakly contraction; after that, we obtained the p-common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak P p -property and proved the uniqueness of these points. Also, we presented some examples to prove the validity of our results. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
23 pages, 295 KiB  
Article
A New Concept of Fixed Point in Metric and Normed Interval Spaces
by Hsien-Chung Wu
Mathematics 2018, 6(11), 219; https://doi.org/10.3390/math6110219 - 25 Oct 2018
Cited by 7 | Viewed by 2140
Abstract
The main aim of this paper is to propose the concept of so-called near fixed point and establish many types of near fixed point theorems in the set of all bounded and closed intervals in R . The concept of null set will [...] Read more.
The main aim of this paper is to propose the concept of so-called near fixed point and establish many types of near fixed point theorems in the set of all bounded and closed intervals in R . The concept of null set will be proposed in order to interpret the additive inverse element in the set of all bounded closed intervals. Based on the null set, the concepts of metric interval space and normed interval space are proposed, which are not the conventional metric and normed spaces. The concept of near fixed point is also defined based on the null set. In this case, we shall establish many types of near fixed point theorems in the metric and normed interval spaces. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
9 pages, 245 KiB  
Article
Some Results on S-Contractions of Type E
by Andreea Fulga and Erdal Karapınar
Mathematics 2018, 6(10), 195; https://doi.org/10.3390/math6100195 - 09 Oct 2018
Cited by 6 | Viewed by 2118
Abstract
In this manuscript, we consider the compositions of simulation functions and E-contraction in the setting of a complete metric space. We investigate the existence and uniqueness of a fixed point for this composite form. We give some illustrative examples and provide an [...] Read more.
In this manuscript, we consider the compositions of simulation functions and E-contraction in the setting of a complete metric space. We investigate the existence and uniqueness of a fixed point for this composite form. We give some illustrative examples and provide an application. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
7 pages, 239 KiB  
Article
Controlled Metric Type Spaces and the Related Contraction Principle
by Nabil Mlaiki, Hassen Aydi, Nizar Souayah and Thabet Abdeljawad
Mathematics 2018, 6(10), 194; https://doi.org/10.3390/math6100194 - 08 Oct 2018
Cited by 150 | Viewed by 6208
Abstract
In this article, we introduce a new extension of b-metric spaces, called controlled metric type spaces, by employing a control function α ( x , y ) of the right-hand side of the b-triangle inequality. Namely, the triangle inequality in the [...] Read more.
In this article, we introduce a new extension of b-metric spaces, called controlled metric type spaces, by employing a control function α ( x , y ) of the right-hand side of the b-triangle inequality. Namely, the triangle inequality in the new defined extension will have the form, d ( x , y ) α ( x , z ) d ( x , z ) + α ( z , y ) d ( z , y ) , for   all x , y , z X . Examples of controlled metric type spaces that are not extended b-metric spaces in the sense of Kamran et al. are given to show that our extension is different. A Banach contraction principle on controlled metric type spaces and an example are given to illustrate the usefulness of the structure of the new extension. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
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