Three-Step Iterative Scheme for Solvability of Generalized Quasi-Variational Like Inclusions in Hilbert spaces

Mohd Iqbal Bhat, Bisma Zahoor

Abstract

In this paper, we consider the system of generalized nonlinear variational-like inclusions in Hilbert spaces. In particular, system of generalized nonlinear variational-like inclusions reduces to a variational inclusion, an extension of variational inclusion studied by Hassouni and Moudafi. Using fixed-point technique, we develop a three-step iterative algorithm for solving the system of generalized nonlinear variational-like inclusions. Further, we prove the existence of solution and discuss convergence criteria for the approximate solution of the system of generalized nonlinear variational-like inclusions. Our three-step iterative algorithm and its convergence results are new and the theorems presented in this paper improve and unify many known results in the literature as well.