scholarly journals Convergence and stability of generalized φ-weak contraction mapping in CAT(0) spaces

2017 ◽  
Vol 15 (1) ◽  
pp. 1063-1074
Author(s):  
Kyung Soo Kim
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Weak Contraction ◽  
Iterative Schemes ◽  
Convergence And Stability

Abstract The aim of this paper is to prove some fixed point results for generalized φ-weak contraction mapping and study a new concept of stability which is called comparably almost T-stable by using iterative schemes in CAT(0) spaces.

scholarly journals PEMETAAN KONTRAKTIF LEMAH MULTIVALUED DI RUANG METRIK PARSIAL

2017 ◽  
Vol 9 (2) ◽  
pp. 1
Author(s):  
Sagita Charolina Sihombing ◽  
Ety Septiati
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Multivalued Mapping ◽  
Contraction Mapping ◽  
Hausdorff Metric ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Weak Contraction

In this paper, we study the existence of fixed point of the φ-weak contraction mapping in the complete partial metric space for multivalued mapping. Distance calculations are performed using Hausdorff metric. The result obtained in this paper is an extension of similar result for single valued mapping.

scholarly journals An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Jong Kyu Kim ◽  
Qiang Lu ◽  
Bin Du
Keyword(s):  
Fixed Point ◽  
Convergence Rate ◽  
Contraction Mapping ◽  
Nonexpansive Mappings ◽  
Positive Influence ◽  
Iteration Scheme ◽  
Contraction Mappings ◽  
Iterative Schemes ◽  
Comparison Results ◽  
The Given

This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results.

scholarly journals Coupled Fixed Point Theorems for Weak Contraction Mappings underF-Invariant Set

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Wutiphol Sintunavarat ◽  
Yeol Je Cho ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Invariant Set ◽  
Mixed Monotone Property ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Monotone Property ◽  
Nonlinear Contraction

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems.

scholarly journals Some Fixed-Point Results for a -Weak Contraction in -Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Complete Metric Spaces

We introduce the concepts of a -weak contraction mapping of types and and we establish some fixed point theorems for a -weak contraction mapping of types and in complete -metric spaces. Our results generalize several well-known comparable results in the literature.

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.

Fixed point theorems for generalized weak contraction mapping in generating space of b-dislocated metric spaces

2020 ◽  
pp. 2150120
Author(s):  
Reena Jain
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Dislocated Metric Space ◽  
Generalized Weak Contraction ◽  
Dislocated Metric

In this paper, the concept of generalized weak contraction mapping in the setting of generating space of [Formula: see text]-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.

scholarly journals The Convex (\delta,L) Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language

2019 ◽  
pp. 157-169
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Contraction Mapping ◽  
Best Proximity Point ◽  
The Other ◽  
Weak Contraction ◽  
Open Problems ◽  
Contraction Mapping Theorem ◽  
Convex Contractions ◽  
Graphic Language

Let $(X,d)$ be a metric space. A map $T:X \mapsto X$ is said to be a $(\delta,L)$ weak contraction [1] if there exists $\delta \in (0,1)$ and $L\geq 0$ such that the following inequality holds for all $x,y \in X$: $d(Tx,Ty)\leq \delta d (x,y)+Ld(y,Tx)$ On the other hand, the idea of convex contractions appeared in [2] and [3]. In the first part of this paper, motivated by [1]-[3], we introduce a concept of convex $(\delta,L)$ weak contraction, and obtain a fixed point theorem associated with this mapping. In the second part of this paper, we consider the map is a non-self map, and obtain a best proximity point theorem. Finally, we leave the reader with some open problems.

scholarly journals Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

SOME FIXED POINT RESULTS FOR A GENERALIZED $\psi$-WEAK CONTRACTION MAPPINGS IN b-METRIC SPACES

2021 ◽  
Vol 10 (5) ◽  
pp. 2449-2468
Author(s):  
E. Bashayreh ◽  
A. Talafhah ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Contraction Mappings

In this paper, we will present the definitions and notation of generalized $\psi$-weak contraction mappings in b-metric spaces, and establish some results besides the most important properties of fixed point in orbitally complete b-metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we generalize the results of Shatanawi [7]. Some examples are given to illustrate the useability of our results.

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