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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

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, 2022. "Graph Convergence and Iterative Approximation of Solution of a Set‐Valued Variational Inclusions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4540369
    DOI: 10.1155/2022/4540369
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    References listed on IDEAS

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    1. Jinlin Guan & Changsong Hu, 2013. "A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, August.
    2. Shamshad Husain & Sanjeev Gupta & Vishnu Narayan Mishra, 2013. "Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions," Journal of Mathematics, Hindawi, vol. 2013, pages 1-10, June.
    3. Jinlin Guan & Changsong Hu, 2013. "A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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