scholarly journals Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
G. C. Ugwunnadi ◽  
Bashir Ali
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Equilibrium Problem ◽  
Iterative Process ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Common Solution ◽  
Convergence Results

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Habtu Zegeye ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Important Class ◽  
Reflexive Banach Spaces ◽  
Nonlinear Operators ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals A Note on “Common Fixed Point of Multistep Noor Iteration with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings”

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Satit Saejung ◽  
Suthep Suantai ◽  
Pongsakorn Yotkaew
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Convergence Results ◽  
Special Case

The purpose of this paper is to give a general and short principle for proving some convergence results of certain types of iterative sequences. A small gap in the paper by Imnang and Suantai (2009) is discussed and corrected. Finally, we prove that the generalized asymptotically quasi-nonexpansive mappings in the sense of Lan (2006) are nothing but asymptotically quasi-nonexpansive. Hence several results concerning these mappings become a special case of the known ones.

scholarly journals Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces

2005 ◽  
Vol 2005 (10) ◽  
pp. 1643-1653 ◽  
Author(s):  
Hafiz Fukhar-Ud-Din ◽  
Abdul Rahim Khan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unbounded Domain ◽  
Iterative Process ◽  
Error Term ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Finite Family ◽  
Iterative Sequence ◽  
Uniformly Convex

We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappings is unbounded, (ii) the iterative sequence contains an error term.

scholarly journals Convergence of implicit iterative process for a finite family of I-nonexpansive mappings

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Seyit Temir ◽  
Goknur Aykanat
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family

AbstractWe prove that an implicit iterative process converges weakly and strongly to a common fixed point of a finite family of

Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Yekini Shehu ◽  
Ferdinard U. Ogbuisi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Finite System ◽  
Iterative Sequence ◽  
Common Solution ◽  
System Of Equilibrium Problems

AbstractIn this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which also solves a finite system of equilibrium problems in a reflexive real Banach space. We further prove that our iterative sequence converges strongly to a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which is also a common solution to a finite system of equilibrium problems. Our result extends many recent and important results in the literature.

scholarly journals Modified three step iterative process with errors for common fixed point of generalized asymptotically quasi-nonexpansive mappings

2012 ◽  
Vol 43 (4) ◽  
pp. 577-586
Author(s):  
Seyit Temir ◽  
Hükmi Kızıltunc
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Results ◽  
The Common

In this paper we introduce to modified three step iterative process with errors for approximating the common fixed point for generalized asymptotically quasi-nonexpansive mappings and prove some strong convergence results for the iterative sequences iterations with errors in real Banach spaces. The results obtained in this paper extend and improve the recent ones announced by Lan \cite{Lan}, Nantadilok \cite{Nan}, Saluja and Nashine \cite{SN} and Yang et all. \cite{LY} and many others.

scholarly journals Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

2016 ◽  
Vol 15 (1) ◽  
pp. 79-96
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Finite Family ◽  
Common Element ◽  
Common Solution ◽  
Convergence Results ◽  
Generalized Equilibrium

AbstractIn this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.

Implicit iterative process for common fixed point of a finite family of asymptotically nonexpansive mappings

2008 ◽  
Vol 45 (2) ◽  
pp. 235-250
Author(s):  
Feng Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration

The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [1,2,4–9,11–15].

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