On the Convergence of the Yosida–Cayley Variational Inclusion Problem with the XOR Operation and Inertial Extrapolation Scheme

Arifuzzaman, Syed Shakaib Irfan and Iqbal Ahmad ()
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Arifuzzaman: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, UP, India
Syed Shakaib Irfan: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, UP, India
Iqbal Ahmad: Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia

Mathematics, 2025, vol. 13, issue 15, 1-29

Abstract: This article studies the structure and properties of real-ordered Hilbert spaces, highlighting the roles of the XOR and XNOR logical operators in conjunction with the Yosida and Cayley approximation operators. These fundamental elements are utilized to formulate the Yosida–Cayley Variational Inclusion Problem (YCVIP) and its associated Yosida–Cayley Resolvent Equation Problem (YCREP). To address these problems, we develop and examine several solution methods, with particular attention given to the convergence behavior of the proposed algorithms. We prove both the existence of solutions and the strong convergence of iterative sequences generated under the influence of the aforesaid operators. The theoretical results are supported by a numerical result, demonstrating the practical applicability and efficiency of the suggested approaches.

Keywords: algorithms; XOR and XNOR operators; resolvent equation; variational inclusion; numerical result; real-ordered Hilbert space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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