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Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation

Author

Listed:
  • Rais Ahmad

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Imran Ali

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Saddam Husain

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • A. Latif

    (Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ching-Feng Wen

    (Center for Fundamental Science and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
    Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan)

Abstract

In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper.

Suggested Citation

  • Rais Ahmad & Imran Ali & Saddam Husain & A. Latif & Ching-Feng Wen, 2019. "Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation," Mathematics, MDPI, vol. 7(5), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:421-:d:230080
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