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Iterative scheme for a nonexpansive mapping, an η-strictly pseudo-contractive mapping and variational inequality problems in a uniformly convex and 2-uniformly smooth Banach space

DOI: 10.1186/1687-1812-2013-23

Keywords: nonexpansive mapping, strictly pseudo-contractive mapping, variational inequality problem

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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 -strictly pseudo-contractive mappings for every in uniformly convex and 2-uniformly smooth Banach spaces.

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