System of generalized set-valued parametric ordered variational inclusion problems with operator $\oplus$ in ordered Banach spaces
Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 103-119 https://doi.org/10.4134/CKMS.c200148 Published online November 18, 2020 Printed January 31, 2021
Mohammad Akram, Mohammad Dilshad Islamic University of Madinah; University of Tabuk
Abstract : 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.
Supported by : This work is financially supported by The Deanship of Scientific Research (DSR), Islamic University of Madinah, KSA, under project number 103
