Abstract
The purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being also zeros of anm-accretive operatorAin the setting of real uniformly convex and 2-uniformly smooth Banach spaceX. Here the modified hybrid steepest-descent methods are based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descent algorithms for finding a common element of the solution set of the GSVI and the setA-1(0)of zeros ofAinX. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
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