Regularized projection method of solving split system of fixed point set constraint equilibrium problems in real Hilbert space

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.

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A New Iterative Method for Equilibrium Problems and Fixed Point Problems

Abstract and Applied Analysis ◽

10.1155/2013/178053 ◽

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

Journal of Applied Mathematics ◽

10.1155/2012/282094 ◽

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.

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

Abstract and Applied Analysis ◽

10.1155/2011/276874 ◽

2011 ◽

Vol 2011 ◽

pp. 1-13 ◽

Cited By ~ 3

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.

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

Journal of Applied Mathematics ◽

10.1155/2012/154968 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21 ◽

Cited By ~ 2

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.

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

Abstract and Applied Analysis ◽

10.1155/2012/161897 ◽

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.

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