Existence of Solution and Iterative Approximation of a System of Generalized Variational-Like Inclusion Problems in Semi-inner Product Spaces

Abstract

In this paper, we consider the system of generalized variational-like inclusion problemsin semi-inner product spaces. We define a class of $(H,\varphi)$-$\eta$-monotone operators and its associated class of generalized resolvent operators. Further, using generalized resolvent operator technique, we give the existence of solution of the generalized variational-like inclusion problems. Furthermore, we suggest an iterative iterative algorithm and give the convergence analysis of the sequences generated by the iterative algorithm. The results presented in this paper extend and unify the related known results in the literature.