scholarly journals Corrigendum to “Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces” [Comput. Math. Appl. 59 (2010) 1473–1483]

2011 ◽  
Vol 61 (1) ◽  
pp. 148 ◽  
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings

scholarly journals An inertial iterative algorithm for generalized equilibrium problems and Bregman relatively nonexpansive mappings in Banach spaces

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Mohammad Farid ◽  
Rehan Ali
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Generalized Equilibrium ◽  
Hybrid Iterative Method

AbstractThe aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result.

scholarly journals Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Rabian Wangkeeree ◽  
Hossein Dehghan ◽  
Pakkapon Preechasilp
Keyword(s):  
Strong Convergence ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Generalized Mixed Equilibrium Problem ◽  
Mixed Equilibrium Problem ◽  
Asymptotically Nonexpansive ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.

A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Mann Iteration ◽  
Infinite Dimensional ◽  
Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

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.

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