scholarly journals Accelerated hybrid iterative algorithm for common fixed points of a finite families of countable Bregman quasi-Lipschitz mappings and solutions of generalized equilibrium problem with application

2017 ◽  
Vol 11 (01) ◽  
pp. 108-130
Author(s):  
Jingling Zhang ◽  
Ravi P. Agarwal ◽  
Nan Jiang
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Common Fixed Points ◽  
Generalized Equilibrium Problem ◽  
Lipschitz Mappings ◽  
Generalized Equilibrium

scholarly journals Algorithms of common solutions for a fixed point of hemicontractive-type mapping and a generalized equilibrium problem

2017 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Habtu Zegeye ◽  
Tesfalem Hadush Meche ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Research Area ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Type Mapping ◽  
Generalized Equilibrium

In this paper, we introduce and study an iterative algorithm for finding a common element of the set of fixed points of a Lipschitz hemicontractive-type multi-valued mapping and the set of solutions of a generalized equilibrium problem in the framework of Hilbert spaces. Our results improve and extend most of the results that have been proved previously by many authors in this research area.

scholarly journals Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Generalized Equilibrium Problem ◽  
Iterative Computation ◽  
Generalized Equilibrium

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given.

scholarly journals A viscosity iterative algorithm for the optimization problem system

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2249-2266 ◽  
Author(s):  
H.R. Sahebi ◽  
S. Ebrahimi
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Optimization Problem ◽  
Common Fixed Points ◽  
Numerical Results ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Mixed Equilibrium Problem

In this paper, we suggest and analysis a viscosity iterative algorithm for finding a common element of the set of solution of a mixed equilibrium problem and the set the of solutions of a variational inequality and all common fixed points of a nonexpansive semigroup. This algorithm strongly converges to an element which solves an optimization problem system. Finally, some examples and numerical results are also given.

scholarly journals Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Nimit Nimana
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Shrinking Projection Method ◽  
Generalized Equilibrium

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.

scholarly journals Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Songnian He ◽  
Jun Guo
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Duality Mapping ◽  
Normalized Duality Mapping ◽  
Uniformly Smooth ◽  
Computational Work

LetCbe a nonempty closed convex subset of a real uniformly smooth Banach spaceX,{Tk}k=1∞:C→Can infinite family of nonexpansive mappings with the nonempty set of common fixed points⋂k=1∞Fix⁡(Tk), andf:C→Ca contraction. We introduce an explicit iterative algorithmxn+1=αnf(xn)+(1-αn)Lnxn, whereLn=∑k=1n(ωk/sn)Tk,Sn=∑k=1nωk,  andwk>0with∑k=1∞ωk=1. Under certain appropriate conditions on{αn}, we prove that{xn}converges strongly to a common fixed pointx*of{Tk}k=1∞, which solves the following variational inequality:〈x*-f(x*),J(x*-p)〉≤0,    p∈⋂k=1∞Fix(Tk), whereJis the (normalized) duality mapping ofX. This algorithm is brief and needs less computational work, since it does not involveW-mapping.

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