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Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space. (30th October 2013)
Record Type:
Journal Article
Title:
Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space. (30th October 2013)
Main Title:
Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
Abstract : 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.