Three-step iterative method for Completely Generalized Set-Valued Strongly Nonlinear Quasi-Variational Inclusions

摘要

In this paper, we introduce and study a new class of completely generalized set-valued strongly nonlinear variational inclusions in Hilbert spaces and establish the equivalence between this variational inclusion and the fixed-point problem by using the resolvent operator technique for maximal monotone mapping. We construct a new three-step iterative algorithm and show the existence of solution for this variational inclusion and the convergence of the iterative method generated by the iterative method.