scholarly journals Invariant approximation results of generalized contractive mappings

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3875-3883
Author(s):  
Ljubomir Ciric ◽  
Sumit Chandok ◽  
Mujahid Abbas
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Periodic Points ◽  
Common Fixed Points ◽  
Weak Contraction ◽  
Contractive Mappings ◽  
Invariant Approximation

Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243] extended the concept of F- contraction mapping introduced in [21], to two mappings. The aim of this paper is to introduce the notion of a generalized F1- weak contraction mapping and to study sufficient conditions for the existence of common fixed points for such class of mappings. As applications, related invariant approximation results are derived. The results obtained herein unify, generalize and complement various known results in the literature.

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>

scholarly journals Fixed point results for Ciric typeweak contraction in metric spaces with applications to partial metric spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1505-1516 ◽  
Author(s):  
Binayak Choudhury ◽  
A. Kundu ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
Weak Contraction ◽  
Control Functions ◽  
Partial Metric Spaces

Partial metric spaces are generalizations of metric spaces which allow for non-zero self-distances. The need for such a definition was felt in the domain of computer science. Fixed point theory has rapidly developed on this space in recent times. Here we define a Ciric type weak contraction mapping with the help of discontinuous control functions and show that in a complete metric space such a function has a fixed point. Our main result has several corollaries and is supported with examples. One of the examples shows that the corollaries are properly contained in the theorem. We give applications of our results in partial metric spaces.

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 Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Mujahid Abbas ◽  
Bashir Ali ◽  
Yusuf I. Suleiman
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Common Solution ◽  
Contractive Mappings ◽  
Multiplicative Metric Spaces

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.

scholarly journals Some Fixed Point Theory Results for the Interpolative Berinde Weak Operator

2020 ◽  
pp. 253-271 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Picard Iteration ◽  
Partial Metric ◽  
Weak Contraction ◽  
Nonlinear Anal ◽  
Partial Metric Spaces ◽  
Weak Operator

Partially inspired by [Erdal Karapinar, Ravi Agarwal and Hassen Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6 (2018), 256] and [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43-53], we introduce a concept of interpolative Berinde weak contraction, and obtain some existence theorems for mappings satisfying such a contractive definition, and some of its extensions.

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.

PERIODIC POINTS OF ${\mathcal C}^1$ MAPS AND THE ASYMPTOTIC LEFSCHETZ NUMBER

1995 ◽  
Vol 05 (05) ◽  
pp. 1369-1373 ◽  
Author(s):  
JOHN GUASCHI ◽  
JAUME LLIBRE
Keyword(s):  
Fixed Point ◽  
Compact Manifold ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Periodic Points ◽  
Lefschetz Number

We study the set of periodic points and the set of periods of different classes of [Formula: see text] self maps of a compact manifold. We give sufficient conditions in order that these sets be infinite. Our main tools are the Lefschetz fixed point theory and homology.

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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