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-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions

Author

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  • Rais Ahmad
  • Mohd Dilshad
  • Mu-Ming Wong
  • Jen-Chin Yao

Abstract

The purpose of this paper is to introduce a new -cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with -cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.

Suggested Citation

  • Rais Ahmad & Mohd Dilshad & Mu-Ming Wong & Jen-Chin Yao, 2011. "-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-12, August.
    • Handle: RePEc:hin:jnlaaa:261534
    DOI: 10.1155/2011/261534
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    Cited by:

    1. Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.

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