ALGORITHM OF SOLUTIONS FOR A SYSTEM OF GENERALIZED MIXED IMPLICIT QUASI-VARIATIONAL INCLUSIONS INVOLVING $h$-$\eta$-MAXIMAL MONOTONE MAPPINGS

Abstract

In this paper, we introduce a new class of $h$-$\eta$-maximal monotone mappings and a new system of generalized mixed implicit quasi-variational inclusions involving set-valued mappings and $h$-$\eta$-maximal monotone mappings. By using resolvent operator technique of $h$-$\eta$-maximal monotone mappings, A new iterative algorithm to compute approximate solutions of the system is suggested and analyzed. The convergence of the iterative sequence generated by the new algorithm is also proved. These results generalize many known results in literature.