A Krasnoselskii-Type Algorithm For Approximating Solutions Of Variational Inequality Problems And Convex Feasibility Problems

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ABSTRACT

A Krasnoselskii-type algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, k-Lipschitz map and solutions of a convex feasibility problem involving a countable family of relatively nonexpansive maps is studied in a uniformly smooth and 2-uniformly convex real Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented.

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