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Cayley Inclusion Problem Involving XOR-Operation

Author

Listed:
  • Imran Ali

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

  • Rais Ahmad

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

  • 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 study an absolutely new problem, namely, the Cayley inclusion problem which involves the Cayley operator and a multi-valued mapping with XOR-operation. We have shown that the Cayley operator is a single-valued comparison and it is Lipschitz-type-continuous. A fixed point formulation of the Cayley inclusion problem is shown by using the concept of a resolvent operator as well as the Yosida approximation operator. Finally, an existence and convergence result is proved. An example is constructed for some of the concepts used in this work.

Suggested Citation

  • Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:302-:d:216955
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    References listed on IDEAS

    as
    1. N. X. Tan, 2004. "On the Existence of Solutions of Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 619-638, December.
    2. 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.
    3. Q. H. Ansari & J. C. Yao, 2001. "Iterative Schemes for Solving Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 527-541, March.
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    Cited by:

    1. Rais Ahmad & Imran Ali & Xiao-Bing Li & Mohd. Ishtyak & Ching-Feng Wen, 2019. "System of Multi-Valued Mixed Variational Inclusions with XOR-Operation in Real Ordered Uniformly Smooth Banach Spaces," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    2. Javid Iqbal & Arvind Kumar Rajpoot & Monirul Islam & Rais Ahmad & Yuanheng Wang, 2022. "System of Generalized Variational Inclusions Involving Cayley Operators and XOR-Operation in q -Uniformly Smooth Banach Spaces," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    3. Imran Ali & Haider Abbas Rizvi & Ramakrishnan Geetha & Yuanheng Wang, 2023. "A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with S -Iterative Algorithm," Mathematics, MDPI, vol. 11(6), pages 1-20, March.

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