International Journal of Nonlinear Analysis and Applications

$H(.,.)$-$\varphi$-$\eta$-accretive operator with an application to a system of generalized variational inclusion problems in $q$-uniformly smooth Banach spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Kashmir South Campus, Anantnag-192101, J & K, India

2 Department of Mathematics, Cluster University, Srinagar-190008, J & K, India

Abstract

In this paper, we study a new system of generalized variational-like inclusion problems involving generalized $H(\cdot,\cdot)$-$\varphi$-$\eta$-accretive operators in real $q$-uniformly smooth Banach spaces. We define the resolvent operator associated with $H(\cdot,\cdot)$-$\varphi$-$\eta$-accretive operator and prove it is single-valued and Lipschitz continuous. Moreover, we suggest a perturbed Mann-type iterative algorithm with errors for approximating the solution of a system of generalized variational-like inclusion problems. Furthermore, we discuss the convergence and stability analysis of the iterative sequence generated by the algorithm.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 181-195
  • Receive Date: 04 December 2021
  • Revise Date: 28 September 2022
  • Accept Date: 30 September 2022