Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros ofm-Accretive Operators in Banach Spaces

摘要

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 beingalso zeros of anm-accretive operatorAin the setting of real uniformly convex and 2-uniformlysmooth Banach spaceX. Here the modified hybrid steepest-descent methods are based onKorpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descentalgorithms 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 thecorresponding results announced in the earlier and very recent literature.