On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems

Abstract

In a real Banach space, let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of countably many nonexpansive mappings. In this article, we introduce a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. Strong convergence of the suggested method to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions is established.

Keywords

• generalized extragradient implicit method
• general system of variational inequalities
• variational inclusion
• common fixed point problem
• 49j30
• 47h09
• 47j20
• 49m05