Abstract
In this paper, we introduce an iterative scheme by the modification of Mann's iteration process for finding a common element of the set of solutions of a finite family of variational inequality problems and the set of fixed points of an η-strictly pseudo-contractive mapping and a nonexpansive mapping. Moreover, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of ηi-strictly pseudo-contractive mappings for every i =1 , 2, ... , N in uniformly convex and 2-uniformly smooth Banach spaces.
Highlights
Let E be a Banach space with its dual space E* and let C be a nonempty closed convex subset of E
In this paper, motivated by Theorems . , . and . , we prove a strong convergence theorem for finding a common element of the set of solutions of a finite family of variational inequality problems and the set of fixed points of a nonexpansive mapping and an η-strictly pseudo-contractive mapping in uniformly convex and -uniformly smooth spaces
By using our main result, we prove a strong convergence theorem for finding a common element of the set of fixed points of a finite family of ηi-strictly pseudocontractive mappings for every i =, . . . , N in uniformly convex and -uniformly smooth Banach spaces
Summary
Let E be a Banach space with its dual space E* and let C be a nonempty closed convex subset of E.
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