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 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 Shrinking Projection Method of Common Fixed Point Problems for Discrete Asymptotically Strictly Pseudocontractive Semigroups and Mixed Equilibrium Problems in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pattanapong Tianchai
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

This paper is concerned with a common element of the set of common fixed point for a discrete asymptotically strictly pseudocontractive semigroup and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method which extends and improves the corresponding ones due to Kim [Proceedings of the Asian Conference on Nonlinear Analysis and Optimization (Matsue, Japan, 2008), 139–162].

scholarly journals Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Kamonrat Sombut ◽  
Somyot Plubtieng
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Split Feasibility Problems ◽  
Mild Conditions ◽  
Weak Convergence Theorem ◽  
Split Feasibility

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.

scholarly journals Shrinking Projection Method of Fixed Point Problems for Asymptotically Pseudocontractive Mapping in the Intermediate Sense and Mixed Equilibrium Problems in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Pattanapong Tianchai
Keyword(s):  
Fixed Point ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Common Element ◽  
Pseudocontractive Mapping ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
Asymptotically Pseudocontractive Mapping

This paper is concerned with a common element of the set of fixed point for an asymptotically pseudocontractive mapping in the intermediate sense and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method, which extends and improves that of Qin et al. (2010) and many others.

A synthetic algorithm for families of demicontractive and nonexpansive mappings and equilibrium problems

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5891-5908
Author(s):  
Ali Abkara ◽  
Mohsen Shekarbaigia
Keyword(s):  
Fixed Points ◽  
Rate Of Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Common Element ◽  
Numerical Examples ◽  
Demicontractive Mappings

We study the rate of convergence of a new synthetic algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a pair of nonexpansive mappings and two finite families of demicontractive mappings. We then provide some numerical examples to illustrate our main result and the proposed algorithm.

scholarly journals Strong convergent iterative techniques for 2-generalized hybrid mappings and split equilibrium problems

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5851-5862
Author(s):  
Jing Zhao ◽  
Yunshui Liang ◽  
Zhenhai Liu
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Split Equilibrium Problem ◽  
Iterative Techniques ◽  
Numerical Example ◽  
Common Solution

In this paper, we suggest a new iterative scheme for finding a common element of the set of solutions of a split equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in Hilbert spaces. We show that the iteration converges strongly to a common solution of the considered problems. A numerical example is illustrated to verify the validity of the proposed algorithm. The results obtained in this paper extend and improve some known results in the literature.

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