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Search Results (5)

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Keywords = Cayley–Yosida Operators

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29 pages, 476 KB  
Article
On the Convergence of the Yosida–Cayley Variational Inclusion Problem with the XOR Operation and Inertial Extrapolation Scheme
by Arifuzzaman, Syed Shakaib Irfan and Iqbal Ahmad
Mathematics 2025, 13(15), 2447; https://doi.org/10.3390/math13152447 - 29 Jul 2025
Cited by 3 | Viewed by 715
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) [...] Read more.
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. Full article
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24 pages, 434 KB  
Article
Three-Step Iterative Methodology for the Solution of Extended Ordered XOR-Inclusion Problems Incorporating Generalized Cayley–Yosida Operators
by Doaa Filali, Imran Ali, Montaser Saudi Ali, Nidal H. E. Eljaneid, Esmail Alshaban and Faizan Ahmad Khan
Mathematics 2025, 13(12), 1969; https://doi.org/10.3390/math13121969 - 14 Jun 2025
Viewed by 754
Abstract
The system of extended ordered XOR-inclusion problems (in short, SEOXORIP) involving generalized Cayley and Yosida operators is introduced and studied in this paper. The solution is obtained in a real ordered Banach space using a fixed-point approach. First, we develop the fixed-point lemma [...] Read more.
The system of extended ordered XOR-inclusion problems (in short, SEOXORIP) involving generalized Cayley and Yosida operators is introduced and studied in this paper. The solution is obtained in a real ordered Banach space using a fixed-point approach. First, we develop the fixed-point lemma for the solution of SEOXORIP. By using the fixed-point lemma, we develop a three-step iterative scheme for obtaining the approximate solution of SEOXORIP. Under the Lipschitz continuous assumptions of the cost mappings, the strong convergence of the scheme is demonstrated. Lastly, we provide a numerical example with a convergence graph generated using MATLAB 2018a to verify the convergence of the sequence generated by the proposed scheme. Full article
(This article belongs to the Special Issue Advances in Mathematical Analysis and Inequalities)
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17 pages, 432 KB  
Article
Three-Step Iterative Algorithm for the Extended Cayley–Yosida Inclusion Problem in 2-Uniformly Smooth Banach Spaces: Convergence and Stability Analysis
by Imran Ali, Yuanheng Wang and Rais Ahmad
Mathematics 2024, 12(13), 1977; https://doi.org/10.3390/math12131977 - 26 Jun 2024
Cited by 1 | Viewed by 2398
Abstract
In this article, we investigate and study an extended Cayley–Yosida inclusion problem. We show that our problem is equivalent to a fixed-point equation. Based on the fixed-point equation, we develop a three-step iterative algorithm to solve our problem. Finally, we illustrate the convergence [...] Read more.
In this article, we investigate and study an extended Cayley–Yosida inclusion problem. We show that our problem is equivalent to a fixed-point equation. Based on the fixed-point equation, we develop a three-step iterative algorithm to solve our problem. Finally, we illustrate the convergence of the proposed algorithm with an example, computational table, and convergence graph by using MATLAB 2018b. Full article
(This article belongs to the Special Issue Advanced Research in Functional Analysis and Operator Theory)
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17 pages, 421 KB  
Article
Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space
by Rais Ahmad, Mohd Ishtyak, Arvind Kumar Rajpoot and Yuanheng Wang
Mathematics 2022, 10(21), 4131; https://doi.org/10.3390/math10214131 - 5 Nov 2022
Cited by 2 | Viewed by 2008
Abstract
In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that our system admits a unique solution by [...] Read more.
In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that our system admits a unique solution by using the properties of q-uniformly smooth Banach space, and we discuss the convergence criteria for sequences generated by iterative algorithm. Two examples are constructed, and an application is provided. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications)
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12 pages, 242 KB  
Article
Cayley Inclusion Problem Involving XOR-Operation
by Imran Ali, Rais Ahmad and Ching-Feng Wen
Mathematics 2019, 7(3), 302; https://doi.org/10.3390/math7030302 - 25 Mar 2019
Cited by 16 | Viewed by 4399
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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