A New Two-Step Iterative Algorithm and $H(.,.)$-Mixed Mappings for Solving a System of Variational Inclusions

Abstract

A system of generalized mixed variational inclusion problem (SGMVIP) is considered involving $H(.,.)$-mixed mappings in $q$-uniformly smooth Banach spaces. By means of proximal-point mapping method, the existence of solution of this system of variational inclusions is given. A new two-step iterative algorithm is proposed for solving SGMVIP. Strong convergence of the proposed algorithm is given.

Keywords

• system of generalized mixed variational inclusion problem
• h(. , .)-mixed mappings
• proximal-point mapping