scholarly journals General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Peichao Duan ◽  
Aihong Wang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by many others.

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 Strong Convergence Theorems for Equilibrium Problems andk-Strict Pseudocontractions in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dao-Jun Wen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Common Element ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed point of a finite family ofk-strictly pseudo-contractive nonself-mappings. Strong convergence theorems are established in a real Hilbert space under some suitable conditions. Our theorems presented in this paper improve and extend the corresponding results announced by many others.

scholarly journals Strong Convergence Results of Split Equilibrium Problems and Fixed Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li-Jun Zhu ◽  
Hsun-Chih Kuo ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Convergence Results

In this paper, we investigate the split equilibrium problem and fixed point problem in Hilbert spaces. We propose an iterative scheme for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are all pseudocontractive. We show that the suggested scheme converges strongly to a solution of the considered problem.

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 Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Pseudocontractive Mappings ◽  
Strict Pseudocontraction ◽  
Strictly Pseudocontractive Mappings

We prove a strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces. We also provide some applications of the main theorem to find a common element of the set of fixed points of a strict pseudocontraction and the set of solutions of an equilibrium problem in Hilbert spaces. The results extend and improve the recent ones announced by Marino and Xu (2007) and others.

scholarly journals Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family ofki-Strictly Pseudocontractive Mapping in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Haitao Che ◽  
Meixia Li ◽  
Xintian Pan
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Element ◽  
Strictly Pseudocontractive Mapping ◽  
Pseudocontractive Mappings ◽  
Definition Of ◽  
Strictly Pseudocontractive Mappings

We first extend the definition of Wnfrom an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family ofki-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

scholarly journals Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Aihong Wang
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Pseudocontractive Mappings ◽  
Viscosity Approximation Methods

We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of the solutions of the equilibrium problem and the set of fixed points of infinitely strict pseudocontractive mappings. Strong convergence theorems are established in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently.

scholarly journals Extragradient methods with CQ technique for fixed point problems and equilibrium problems

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4783-4793
Author(s):  
Zhangsong Yao ◽  
Yeong-Cheng Liou ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Fixed Point Problems ◽  
Common Element ◽  
Extragradient Methods ◽  
Extragradient Algorithm

In this paper, we study iterative algorithms for solving fixed point problems and equilibrium problems in Hilbert spaces. We present an extragradient algorithm with CQ technique for finding a common element of the fixed points of pseudocontractive operators and the solutions of pseudomonotone equilibrium problems. Strong convergence result of the proposed algorithm is proved.

scholarly journals A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Pakkapon Preechasilp
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Solution

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature.

scholarly journals Some Results on Strictly Pseudocontractive Nonself-Mappings and Equilibrium Problems in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yan Hao ◽  
Sun Young Cho
Keyword(s):  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Common Elements ◽  
Projection Algorithms ◽  
Convergence Theorems

An equilibrium problem and a strictly pseudocontractive nonself-mapping are investigated. Strong convergence theorems of common elements are established based on hybrid projection algorithms in the framework of real Hilbert spaces.

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