scholarly journals A Constructive Scheme for a Common Coupled Fixed Point Problems in Hilbert Space

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1717
Author(s):  
Kyung Soo Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Coupled Fixed Point ◽  
Common Coupled Fixed Point ◽  
Potential Applications ◽  
Fixed Point Iterations ◽  
Common Coupled Fixed Points ◽  
Coupled Fixed Points

Coupled fixed points have become the focus of interest in recent times, especially for their potential applications. Very recently, the idea of common coupled fixed point iterations has been introduced for approximating common coupled fixed points in linear spaces. Here, a coupled Mann pair iterative scheme is defined and is applied to the problem of finding common coupled fixed points of certain mappings. The discussion of the paper is in the context of Hilbert spaces.

scholarly journals COMMON COUPLED FIXED POINTS FOR TWO PAIRS OF w -COMPATIBLE MAPS IN PARTIAL G -METRIC SPACES

2016 ◽  
Vol 12 (2) ◽  
pp. 7-28
Author(s):  
K. P. R. Rao ◽  
G. N. V. Kishore ◽  
S. K. Sadik
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Compatible Mappings ◽  
Compatible Maps ◽  
Coupled Fixed Point Theorem ◽  
Common Coupled Fixed Points ◽  
Coupled Fixed Points

In this paper we prove a unique common coupled fixed point theorem for two pairs of w-compatible mappings satisfying two contractive conditions in partial G-metric spaces. We also furnish an example to support our main theorem.Mathematics Subject Classification: 47H10, 54H25Kathmandu UniversityJournal of Science, Engineering and TechnologyVol. 12, No. 2, 2016, page: 7-28 

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Akbar Azam ◽  
Jamshaid Ahmad ◽  
Cristina Di Bari
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Contraction ◽  
Complex Valued Metric Space ◽  
The Common ◽  
Complex Valued ◽  
Common Coupled Fixed Points ◽  
Coupled Fixed Points

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces

2018 ◽  
Vol 19 (2) ◽  
pp. 189 ◽  
Author(s):  
Mortaza Abtahi ◽  
Zoran Kadelburg ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Partially Ordered ◽  
Generalized Metric ◽  
Coupled Fixed Points

<p>New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.</p>

scholarly journals Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 726-742
Author(s):  
Esad Jakupović ◽  
Hashem Masiha ◽  
Zoran Mitrović ◽  
Seyede Razavi ◽  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Point Theory ◽  
C Algebra ◽  
Coupled Fixed Points

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C*-algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.

scholarly journals A Simple Method for Obtaining Coupled Fixed Points of --Contractive Type Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sh. Rezapour ◽  
J. Hasanzade Asl
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Coupled Fixed Point ◽  
Simple Method ◽  
Contractive Type ◽  
Coupled Fixed Points

In 2012, the notion of --contractive type mappings was introduced by Samet, C. Vetro, and P. Vetro. By using a simple method, we give some coupled fixed point results for --contractive type mappings.

Coupled fixed points and coupled best proximity points for cyclic Ćirić type operators

2019 ◽  
Vol 26 (1/2) ◽  
pp. 179-196
Author(s):  
Adrian Magdaş
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Coupled Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Best Proximity Points ◽  
Contraction Type ◽  
Coupled Fixed Points

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

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