Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation
Due to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. The aim of this work is to introduce and study a Yosida complementarity problem, a Yosida variational inequality problem, and...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9362630 |
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| _version_ | 1832551931192541184 |
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| author | Rais Ahmad Arvind Kumar Rajpoot Imran Ali Ching-Feng Wen |
| author_facet | Rais Ahmad Arvind Kumar Rajpoot Imran Ali Ching-Feng Wen |
| author_sort | Rais Ahmad |
| collection | DOAJ |
| description | Due to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. The aim of this work is to introduce and study a Yosida complementarity problem, a Yosida variational inequality problem, and a Yosida proximal operator equation involving XOR-operation. We prove an existence result together with convergence analysis for Yosida proximal operator equation involving XOR-operation. For this purpose, we establish an algorithm based on fixed point formulation. Our approach is based on a proximal operator technique involving a subdifferential operator. As an application of our main result, we provide a numerical example using the MATLAB program R2018a. Comparing different iterations, a computational table is assembled and some graphs are plotted to show the convergence of iterative sequences for different initial values. |
| format | Article |
| id | doaj-art-198ffdeaac8d4c06bd4426afa4e0c677 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-198ffdeaac8d4c06bd4426afa4e0c6772025-02-03T05:59:59ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/9362630Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-OperationRais Ahmad0Arvind Kumar Rajpoot1Imran Ali2Ching-Feng Wen3Department of MathematicsDepartment of MathematicsDepartment of MathematicsCenter for Fundamental ScienceDue to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. The aim of this work is to introduce and study a Yosida complementarity problem, a Yosida variational inequality problem, and a Yosida proximal operator equation involving XOR-operation. We prove an existence result together with convergence analysis for Yosida proximal operator equation involving XOR-operation. For this purpose, we establish an algorithm based on fixed point formulation. Our approach is based on a proximal operator technique involving a subdifferential operator. As an application of our main result, we provide a numerical example using the MATLAB program R2018a. Comparing different iterations, a computational table is assembled and some graphs are plotted to show the convergence of iterative sequences for different initial values.http://dx.doi.org/10.1155/2021/9362630 |
| spellingShingle | Rais Ahmad Arvind Kumar Rajpoot Imran Ali Ching-Feng Wen Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation Journal of Mathematics |
| title | Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation |
| title_full | Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation |
| title_fullStr | Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation |
| title_full_unstemmed | Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation |
| title_short | Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation |
| title_sort | yosida complementarity problem with yosida variational inequality problem and yosida proximal operator equation involving xor operation |
| url | http://dx.doi.org/10.1155/2021/9362630 |
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