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Graph Convergence and Iterative Approximation of Solution of a Set-Valued Variational Inclusions

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  • Faizan Ahmad Khan
  • Sanjeev Gupta
  • Valerii Obukhovskii

Abstract

In this article, first, we introduce a class of proximal-point mapping associated with generalized αiβj-Hp.,.,…-accretive mapping. Further, we discuss the graph convergence of generalized αiβj-Hp.,.,…-accretive mapping. As an application, we consider a set-valued variational inclusion problem (SVIP) in real Banach spaces. Furthermore, we propose an iterative scheme involving the above class of proximal-point mapping to find a solution of SVIP and discuss its convergence under some convenient assumptions. An example is constructed and demonstrated few graphics in support of our main results.

Suggested Citation

  • Faizan Ahmad Khan & Sanjeev Gupta & Valerii Obukhovskii, 2022. "Graph Convergence and Iterative Approximation of Solution of a Set-Valued Variational Inclusions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-18, November.
    • Handle: RePEc:hin:jjmath:4540369
    DOI: 10.1155/2022/4540369
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