Solving Variational Inequalities Involving Nonexpansive Type Mappings
نویسندگان
چکیده
The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of nonexpansive mappings or the set of fixed points of pseudocontractive mappings. Our convergence analysis covers proximal point algorithm for finding zeros accretive operators as well as functional Helpern algorithm for finding fixed points of nonexpansive mappings in Banach spaces. Our results improve a number of results concerned with viscosity approximation methods in the context of weakly contraction mappings.
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