System of Set-Valued Nonlinear Generalized Variational Inclusion Problems in Banach Spaces

Abstract

In this paper, we consider a system of set-valued nonlinear generalized variational inclusion problems (SNGVIP) in $q$-uniformly smooth Banach spaces. We define a class of $H(·,·)$-mixed mappings and its associated class of resolvent operators. Further, using proximal-point mapping method, we suggest an iterative algorithm for finding the solution of the system of set-valued nonlinear generalized variational inclusion problems. Furthermore, we discuss the convergence criteria of the sequences generated by the iterative algorithm.