Abstract
Let C be a nonempty, closed and convex subset of a 2-uniformly convex and uniformly smooth real Banach space E. Let T: C→ C be relatively nonexpansive mapping and let A i : C→ E* be L i -Lipschitz monotone mappings, for i = 1,2. In this paper, we introduce and study an iterative process for finding a common point of the fixed point set of a relatively nonexpansive mapping and the solution set of variational inequality problems for A 1 and A 2. Under some mild assumptions, we show that the proposed algorithm converges strongly to a point in \({F(T)\cap VI(C, A_1)\cap VI(C, A_2)}\). Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
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Tufa, A.R., Zegeye, H. An algorithm for finding a common point of the solutions of fixed point and variational inequality problems in Banach spaces. Arab. J. Math. 4, 199–213 (2015). https://doi.org/10.1007/s40065-015-0130-0
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DOI: https://doi.org/10.1007/s40065-015-0130-0