(A(., .), η)-MONOTONE MAPPINGS AND A SYSTEM OF GENERALIZED SET-VALUED VARIATIONAL-LIKE INCLUSION PROBLEM

By

Sumeera Shafiᵃ¹ and Vishnu Narayan Mishrabᵇ²

ᵃDepartment of Mathematics, University of Kashmir, Srinagar-190006, India

ᵇDepartment of Mathematics, Indira Gandhi National Tribal University

Lalpur, Amarkantak-484887, Madhya Pradesh, India

Email:¹sumeera.shafi@gmail.com(Sumeera Shafi)

²vishnunarayanmishra@gmail.com(Vishnu Narayan Mishra)

(Received : April 23, 2021 ; In format June 19, 2021 ; Revised in final form : June 30, 2021)

DOI: https://doi.org/10.58250/Jnanabha.2021.51130

Abstract

In this paper, we introduce and study a system of variational inclusions called system of generalized set-valued variational-like inclusion problem involving (A(., .), η)-monotone mappings in real Banach spaces. By means of resolvent operator technique, we prove the existence of solutions for this system of variational inclusions. Further, we suggest an iterative algorithm for finding the approximate solution of this system and discuss the convergence criteria of the sequences generated by the iterative algorithm under some suitable conditions.

2010 Mathematics Subject Classifications: 47H09, 47J20, 49J40.

Keywords and phrases: System of generalized set-valued variational-like inclusion problem, (A(., .), η)-monotone mappings, Resolvent operator, Iterative algorithm, Convergence analysis.

[Download full paper]