scholarly journals A viscosity Cesàro mean approximation method for split generalized vector equilibrium problem and fixed point problem

2015 ◽  
Vol 23 (2) ◽  
pp. 362-370
Author(s):  
K.R. Kazmi ◽  
S.H. Rizvi ◽  
Mohd. Farid
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Approximation Method ◽  
Fixed Point Problem ◽  
Vector Equilibrium Problem ◽  
Point Problem ◽  
Cesàro Mean ◽  
Generalized Vector Equilibrium Problem ◽  
Cesaro Mean ◽  
Vector Equilibrium

scholarly journals Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Dual Space ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Existence Of A Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We study and establish the existence of a solution for a generalized mixed equilibrium problem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature.

scholarly journals Split equality common null point problem for Bregman quasi-nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3917-3932
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Reflexive Banach Spaces

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

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