scholarly journals Best Proximity Point Results inG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
N. Hussain ◽  
A. Latif ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Rich Source ◽  
Point Problem ◽  
Proximal Contraction ◽  
Contraction Mappings

G-metric spaces proved to be a rich source for fixed point theory; however, the best proximity point problem has not been considered in such spaces. The aim of this paper is to introduce certain new classes of proximal contraction mappings and establish the best proximity point theorems for such kind of mappings inG-metric spaces. As a consequence of these results, we deduce certain new best proximity and fixed point results. Moreover, we present an example to illustrate the usability of the obtained results.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3365-3379 ◽  
Author(s):  
Z. Ahmadi ◽  
R. Lashkaripour ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Complete Metric Spaces ◽  
New Class ◽  
Constraint Inequalities ◽  
Weaker Conditions

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

On the theory of fixed point theorems for convex contraction mappings

2015 ◽  
Vol 31 (3) ◽  
pp. 365-371
Author(s):  
VIORICA MURESAN ◽  
◽  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing

Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

scholarly journals On Best Proximity Points under the -Property on Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Point Of View ◽  
Ordered Metric Spaces

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.

scholarly journals Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 541
Author(s):  
Shamoona Jabeen ◽  
Zhiming Zheng ◽  
Mutti-Ur Rehman ◽  
Wei Wei ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Continuity Condition ◽  
Graph Structure ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Cone Metric

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.

scholarly journals Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1350
Author(s):  
Mujahid Abbas ◽  
Rizwan Anjum ◽  
Vasile Berinde
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Differential Inclusions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Point Problem ◽  
Fixed Point Set ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Multivalued Contraction

The purpose of this paper is to introduce the class of enriched multivalued contraction mappings. Both single-valued and multivalued enriched contractions are defined by means of symmetric inequalities. Our main result extends and generalizes the recent result of Berinde and Păcurar (Approximating fixed points of enriched contractions in Banach spaces, Journal of Fixed Point Theory and Applications, 22 (2), 1–10, 2020). We also study a data dependence problem of the fixed point set and Ulam–Hyers stability of the fixed point problem for enriched multivalued contraction mappings. Applications of the results obtained to the problem of the existence of a solution of differential inclusions and dynamic programming are presented.

scholarly journals Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 435-447 ◽  
Author(s):  
Azhar Hussain ◽  
Muhammad Iqbal ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Ordered Metric Spaces ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Auxiliary Functions

In this paper we study the notion of modified Suzuki-Edelstein proximal contraction under some auxiliary functions for non-self mappings and obtain best proximity point theorems in the setting of complete metric spaces. As applications, we derive best proximity point and fixed point results for such contraction mappings in partially ordered metric spaces. Some examples are given to show the validity of our results. Our results extend and unify many existing results in the literature.

scholarly journals On Convergence of Fixed Points in Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yonghong Shen ◽  
Dong Qiu ◽  
Wei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Direction ◽  
Point Theory ◽  
Fuzzy Metric Spaces ◽  
Contraction Mappings ◽  
Fuzzy Metric

We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.

scholarly journals Cyclic Mappings and Further Results in B-Metric-Like Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shengquan Weng ◽  
Quanxin Zhu ◽  
Baoying Du ◽  
Kaibo Shi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Formula Type

Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.

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