scholarly journals Iterative Algorithms with Perturbations for Solving the Systems of Generalized Equilibrium Problems and the Fixed Point Problems of Two Quasi-Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
Rabian Wangkeeree ◽  
Uraiwan Boonkong
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Common Fixed Points ◽  
Common Element ◽  
Fixed Point Set ◽  
Generalized Equilibrium ◽  
Point Set ◽  
The Common

We introduce new iterative algorithms with perturbations for finding a common element of the set of solutions of the system of generalized equilibrium problems and the set of common fixed points of two quasi-nonexpansive mappings in a Hilbert space. Under suitable conditions, strong convergence theorems are obtained. Furthermore, we also consider the iterative algorithms with perturbations for finding a common element of the solution set of the systems of generalized equilibrium problems and the common fixed point set of the super hybrid mappings in Hilbert spaces.

scholarly journals Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Shenghua Wang ◽  
Shin Min Kang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Iterative Algorithms ◽  
Common Fixed Points ◽  
Common Element ◽  
Fixed Point Set ◽  
Point Set

We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.

scholarly journals A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-25
Author(s):  
Rattanaporn Wangkeeree ◽  
Uthai Kamraksa ◽  
Rabian Wangkeeree
Keyword(s):  
Fixed Point ◽  
General Equilibrium ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Strictly Pseudocontractive Mapping ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

We introduce a general composite algorithm for finding a common element of the set of solutions of a general equilibrium problem and the common fixed point set of a finite family of asymptotically nonexpansive mappings in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudocontractive mapping. Our results extend the corresponding recent results of Yao and Liou (2010).

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Tanom Chamnarnpan ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Monotone Mapping ◽  
Iterative Algorithms ◽  
Infinite Family ◽  
Common Element ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

scholarly journals Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Fixed Point Set ◽  
Common Fixed Point Problem ◽  
The Family ◽  
Point Set ◽  
The Common

It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where stands for the common fixed-point set of the family of multivalued nonexpansive mapping .

scholarly journals The System of Mixed Equilibrium Problems for Quasi-Nonexpansive Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Rabian Wangkeeree ◽  
Panatda Boonman
Keyword(s):  
Hilbert Space ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Solution Set ◽  
Common Element ◽  
Fixed Point Set ◽  
Mixed Equilibrium Problems ◽  
Point Set ◽  
Mixed Equilibrium

We first introduce the iterative procedure to approximate a common element of the fixed-point set of two quasinonexpansive mappings and the solution set of the system of mixed equilibrium problem (SMEP) in a real Hilbert space. Next, we prove the weak convergence for the given iterative scheme under certain assumptions. Finally, we apply our results to approximate a common element of the set of common fixed points of asymptotic nonspreading mapping and asymptoticTJmapping and the solution set of SMEP in a real Hilbert space.

scholarly journals Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Suthep Suantai
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problems ◽  
The Common ◽  
System Of Equilibrium Problems

We introduce a new hybrid iterative scheme for finding a common element in the solutions set of a system of equilibrium problems and the common fixed points set of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space.

CONVERGENCE OF ITERATIVE SCHEMES FOR NONEXPANSIVE MAPPINGS

2011 ◽  
Vol 04 (04) ◽  
pp. 671-682 ◽  
Author(s):  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mappings ◽  
Initial Point ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Fixed Point Set ◽  
Iteration Formula ◽  
Point Set ◽  
Implicit Iteration

Let K be a nonempty closed convex subset of a real uniformly convex Banach space X and suppose T : K → K is a nonexpansive mapping with the nonempty fixed point set Fix(T). Let [Formula: see text], [Formula: see text] and [Formula: see text] be sequences in [0, 1] such that [Formula: see text][Formula: see text][Formula: see text] for some constants a, b, α, β, and γ. Let x0 ∈ K be any initial point. Then it is proved that the implicit iteration [Formula: see text] defined by [Formula: see text] converges weakly to a fixed point of T. Furthermore, it is generalized that if [Formula: see text] is a finite family of nonexpansive self-mappings of K with the nonempty common fixed points set [Formula: see text] and if the parameters [Formula: see text], [Formula: see text], and [Formula: see text] satisfy the conditions (0.1), (0.2), (0.3), and [Formula: see text] for some constant c , then the modified implicit iteration [Formula: see text] defined by [Formula: see text] where Tn = Tn(modN), converges weakly to a common fixed point of the family [Formula: see text]. The results presented in this paper improve and extend the corresponding results of Z. Opial [11], S. Reich [13], H.-K. Xu and R. G. Ori [20], and Zhao et al. [21].

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