scholarly journals Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

2021 ◽  
Vol 7 (2) ◽  
pp. 2195-2219
Author(s):  
Muhammad Rafique ◽  
◽  
Talat Nazir ◽  
Mujahid Abbas ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Fuzzy Mathematics ◽  
New Class ◽  
Contractive Mappings ◽  
New Research

<abstract><p>We introduce a new class of generalized graphic fuzzy $ F $- contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.</p></abstract>

New fixed point results in bv(s)-metric spaces

2020 ◽  
Vol 70 (2) ◽  
pp. 441-452
Author(s):  
Tatjana Došenović ◽  
Zoran Kadelburg ◽  
Zoran D. Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Generalized Metric ◽  
The One

Abstract Z. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions in bv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings in bv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric and b-metric spaces. Examples show the usefulness of the obtained results.

Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Hemant Nashine
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Partial Metric ◽  
New Class ◽  
Weakly Contractive Condition ◽  
Partial Metric Spaces ◽  
Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5497-5509 ◽  
Author(s):  
Habes Alsamir ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Kamal Abodyah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Partial Metric ◽  
Partially Ordered ◽  
Partial Metric Spaces ◽  
Contraction Type

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

scholarly journals Pseudo Picard operators on generalized metric spaces

2018 ◽  
Vol 12 (2) ◽  
pp. 389-400 ◽  
Author(s):  
Ishak Altun ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Generalized Metric

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. Jleli and B. Samet: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.

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.

scholarly journals Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Lower Solution ◽  
Existence Of Solution ◽  
Order Ordinary Differential Equation ◽  
Complete Metric Spaces ◽  
First Order ◽  
Contractive Mappings

We establish a fixed point theorem withw-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

Fuzzy relation-theoretic contraction principle

2020 ◽  
pp. 1-11
Author(s):  
Waleed M. Alfaqih ◽  
Based Ali ◽  
Mohammad Imdad ◽  
Salvatore Sessa
Keyword(s):  
Fixed Point ◽  
Fuzzy Sets ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fuzzy Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings ◽  
Fuzzy Fixed Point

In this manuscript, we provide a new and novel generalization of the concept of fuzzy contractive mappings due to Gregori and Sapena [Fuzzy Sets and Systems 125 (2002) 245–252] in the setting of relational fuzzy metric spaces. Our findings possibly pave the way for another direction of relation-theoretic as well as fuzzy fixed point theory. We illustrate several examples to show the usefulness of our proven results. Moreover, we define cyclic fuzzy contractive mappings and utilize our main results to prove a fixed point result for such mappings. Finally, we deduce several results including fuzzy metric, order-theoretic and α-admissible results.

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