scholarly journals Some new observations on fixed point results in rectangular metric spaces with applications to chemical sciences

2021 ◽  
Vol 69 (1) ◽  
pp. 8-30
Author(s):  
Mudasir Younis ◽  
Nicola Fabiano ◽  
Zaid Fadail ◽  
Zoran Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Nonlinear Problems ◽  
Point Theory ◽  
New Approach ◽  
Generalized Metric Spaces ◽  
Picard Sequence ◽  
Open Question

Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this paper is to provide much simpler and shorter proofs of some new results in rectangular metric spaces. Methods: Some standard methods from the fixed point theory in generalized metric spaces are used. Results: The obtained results improve the well-known results in the literature. The new approach has proved that the Picard sequence is Cauchy in rectangular metric spaces. The obtained results are used to prove the existence of solutions to some nonlinear problems related to chemical sciences. Finally, an open question is given for generalized contractile mappings in rectangular metric spaces. Conclusions: New results are given for fixed points in rectangular metric spaces with application to some problems in chemical sciences.

scholarly journals On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2048
Author(s):  
Jelena Vujaković ◽  
Eugen Ljajko ◽  
Slobodan Radojević ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Approach ◽  
Complete Metric Spaces

Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

scholarly journals On Recent Results Concerning F-Contraction in Generalized Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 767 ◽  
Author(s):  
Jelena Vujaković ◽  
Slobodanka Mitrović ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
New Approach ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Type Mapping ◽  
Contraction Type ◽  
Picard Sequence ◽  
Open Question

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

scholarly journals Common Fixed Points in Generalized Metric Spaces with a Graph

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Karim Chaira ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Points Of Coincidence

The aim of this paper is to prove the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings defined on generalized metric spaces with a graph. Our results improve and extend several recent results of metric fixed point theory.

scholarly journals A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 512 ◽  
Author(s):  
Erdal Karapınar ◽  
Panda Kumari ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nash Equilibria ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
New Approach ◽  
Correctness Of Programs

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

scholarly journals Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Mudasir Younis ◽  
Deepak Singh ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Graph Theory ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Nonlinear Problems ◽  
Point Theory ◽  
Open Problems ◽  
Mass System ◽  
Fixed Point Result

The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphical b-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

scholarly journals Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

scholarly journals A new approach on coupled fixed point theory in JS-metric spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 323-336 ◽  
Author(s):  
Tanusri Senapati ◽  
◽  
Lakshmi Kanta Dey ◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
New Approach

scholarly journals Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

2021 ◽  
Vol 37 (2) ◽  
pp. 345-354
Author(s):  
ALEXANDRU-DARIUS FILIP
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

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