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.
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
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