scholarly journals Approximate Equilibrium Problems and Fixed Points

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
H. Mazaheri ◽  
S. A. M. Mohsenalhosseini
Keyword(s):  
Hilbert Space ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Common Element ◽  
Approximate Equilibrium

We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.

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).

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 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 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.

scholarly journals Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhou Yinying ◽  
Cao Jiantao ◽  
Wang Yali
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Common Element

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).

scholarly journals Strong and Weak Convergence Theorems for Equilibrium Problems and Weak Relatively Uniformly Nonexpansive Multivalued Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Zi-Ming Wang
Keyword(s):  
Weak Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Common Element ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
The Common

Equilibrium problem and fixed point problem are considered. A general iterative algorithm is introduced for finding a common element of the set of solutions to the equilibrium problem and the common set of fixed points of two weak relatively uniformly nonexpansive multivalued mappings. Furthermore, strong and weak convergence results for the common element in the two sets mentioned above are established in some Banach space.

scholarly journals Convergence Theorems for Accretive Operators with Nonlinear Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yan-Lai Song ◽  
Lu-Chuan Ceng
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Recent Literature ◽  
Common Element ◽  
Inclusion Problem ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of strict pseudocontractions in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating these common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Further, we consider the problem of finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a strict pseudocontractions.

scholarly journals Explicit Scheme for Fixed Point Problem for Nonexpansive Semigroup and Split Equilibrium Problem in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Pei Zhou ◽  
Gou-Jie Zhao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Explicit Scheme ◽  
Common Element ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem

We establish an iterative method for finding a common element of the set of fixed points of nonexpansive semigroup and the set of split equilibrium problems. Under suitable conditions, some strong convergence theorems are proved. Our works improve previous results for nonexpansive semigroup.

scholarly journals A New Iterative Method for Equilibrium Problems and Fixed Point Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Abdul Latif ◽  
Mohammad Eslamian
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Equilibrium Problems ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Common Element ◽  
Continuous Mappings ◽  
New Iterative Method

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.

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