An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems
In this paper, we introduce a modified form of the <i>G</i>-variational inequality problem, called the combination of <i>G</i>-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element b...
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2024-12-01
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| author | Araya Kheawborisut Atid Kangtunyakarn |
| author_facet | Araya Kheawborisut Atid Kangtunyakarn |
| author_sort | Araya Kheawborisut |
| collection | DOAJ |
| description | In this paper, we introduce a modified form of the <i>G</i>-variational inequality problem, called the combination of <i>G</i>-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a <i>G</i>-nonexpansive mapping and the solution set of the proposed <i>G</i>-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the <i>G</i>-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the <i>G</i>-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings. |
| format | Article |
| id | doaj-art-5122f3caabe9493281ef39698d6dfa01 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5122f3caabe9493281ef39698d6dfa012025-01-10T13:18:19ZengMDPI AGMathematics2227-73902024-12-0113112210.3390/math13010122An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point ProblemsAraya Kheawborisut0Atid Kangtunyakarn1Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandDepartment of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandIn this paper, we introduce a modified form of the <i>G</i>-variational inequality problem, called the combination of <i>G</i>-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a <i>G</i>-nonexpansive mapping and the solution set of the proposed <i>G</i>-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the <i>G</i>-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the <i>G</i>-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings.https://www.mdpi.com/2227-7390/13/1/122the combination of <i>G</i>-variational inequality problemsfixed point problem<i>G</i>-inverse strongly monotone mapping |
| spellingShingle | Araya Kheawborisut Atid Kangtunyakarn An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems Mathematics the combination of <i>G</i>-variational inequality problems fixed point problem <i>G</i>-inverse strongly monotone mapping |
| title | An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems |
| title_full | An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems |
| title_fullStr | An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems |
| title_full_unstemmed | An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems |
| title_short | An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems |
| title_sort | approximation algorithm for the combination of i g i variational inequalities and fixed point problems |
| topic | the combination of <i>G</i>-variational inequality problems fixed point problem <i>G</i>-inverse strongly monotone mapping |
| url | https://www.mdpi.com/2227-7390/13/1/122 |
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