scholarly journals An Alternative Regularization Method for Equilibrium Problems and Fixed Point of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Shuo Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Regularization Method ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Sunny Nonexpansive Retraction

We introduce a new regularization iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping. Then, we prove a strong convergence theorem for nonexpansive mappings to solve a unique solution of the variational inequality and the unique sunny nonexpansive retraction. Our results extend beyond the results of S. Takahashi and W. Takahashi (2007), and many others.

scholarly journals Hybrid subgradient algorithm for equilibrium and fixed point problems by approximation of nonexpansive mapping

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1721-1729
Author(s):  
Seyed Aleomraninejad ◽  
Kanokwan Sitthithakerngkiet ◽  
Poom Kumam
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Expansive Mapping ◽  
Subgradient Algorithm

In this paper anew algorithm considered on a real Hilbert space for finding acommonpoint in the solution set of a class of pseudomonotone equilibrium problem and the set of fixed points of nonexpansive mappings. We produce this algorithm by mappings Tk that are approximations of non-expansive mapping T. The strong convergence theorem of the proposed algorithms is investigated. Our results generalize some recent results in the literature.

scholarly journals A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mei Yuan ◽  
Xi Li ◽  
Xue-song Li ◽  
John J. Liu
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Projection Method ◽  
Convergence Theorem ◽  
Projection Operator ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.

scholarly journals Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Bashir Ali
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem ◽  
Points Approximation

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results.

scholarly journals Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Zhaoli Ma ◽  
Lin Wang ◽  
Yunhe Zhao
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Generalized Mixed Equilibrium Problems ◽  
Asymptotically Nonexpansive ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium

We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.

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