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Mathematics 2019, 7(3), 302;

Cayley Inclusion Problem Involving XOR-Operation

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
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
Author to whom correspondence should be addressed.
Received: 9 February 2019 / Revised: 14 March 2019 / Accepted: 21 March 2019 / Published: 25 March 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
PDF [242 KB, uploaded 25 March 2019]


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. View Full-Text
Keywords: Cayley; Convergence; Resolvent; XOR-operation; Yosida Cayley; Convergence; Resolvent; XOR-operation; Yosida
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ali, I.; Ahmad, R.; Wen, C.-F. Cayley Inclusion Problem Involving XOR-Operation. Mathematics 2019, 7, 302.

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