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

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 Inclusi...

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Bibliographic Details
Main Authors: Arifuzzaman, Syed Shakaib Irfan, Iqbal Ahmad
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/15/2447
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Summary: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.
ISSN:2227-7390