Communications of the
Korean Mathematical Society CKMS

In this article, we study a system of generalized set-valued parametric ordered variational inclusion problems with operator $\oplus$ in ordered Banach spaces. We introduce the concept of the resolvent operator associated with $(\alpha, \lambda)$-ANODSM set-valued mapping and establish the existence theorem of solution for the system of generalized set-valued parametric ordered variational inclusion problems in ordered Banach spaces. In order to prove the existence of solution, we suggest an iterative algorithm and discuss the convergence analysis under some suitable mild conditions.

Keywords: Ordered Banach space, $ANODSM$-set-valued mapping, comparison mapping, ordered variational inclusions, convergence

MSC numbers: Primary 47H06, 49J40

Supported by: This work is financially supported by The Deanship of Scientific Research (DSR), Islamic University of Madinah, KSA, under project number 103