On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme
Abstract In this paper, we provide a simplified proof of the existence of solutions for the system of nonlinear quasi-mixed equilibrium problems studied by Suantai and Petrot (Appl. Math. Lett. 24:308–313, 2011), utilizing Banach’s fixed point theorem. This result remains valid under weaker assumpti...
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2025-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03252-3 |
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| author | Satit Saejung |
| author_facet | Satit Saejung |
| author_sort | Satit Saejung |
| collection | DOAJ |
| description | Abstract In this paper, we provide a simplified proof of the existence of solutions for the system of nonlinear quasi-mixed equilibrium problems studied by Suantai and Petrot (Appl. Math. Lett. 24:308–313, 2011), utilizing Banach’s fixed point theorem. This result remains valid under weaker assumptions through the product space approach. Moreover, we show that the stability analysis of the iterative algorithm proposed in their work (and in (J. Inequal. Appl. 2010:437976, 2010)) contains a flaw, which we address using Ostrowski’s classical result from 1967 (Z. Angew. Math. Mech. 47:77–81, 1967). Finally, we examine and improve the convergence theorem for solving a system of variational inequalities as established by Chang et al. (Appl. Math. Lett. 20:329–334, 2007). |
| format | Article |
| id | doaj-art-c2abf47ac6c34b678779271cb374fbe1 |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-c2abf47ac6c34b678779271cb374fbe12025-01-19T12:43:00ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-01-012025111510.1186/s13660-025-03252-3On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure schemeSatit Saejung0Department of Mathematics, Faculty of Science, Khon Kaen UniversityAbstract In this paper, we provide a simplified proof of the existence of solutions for the system of nonlinear quasi-mixed equilibrium problems studied by Suantai and Petrot (Appl. Math. Lett. 24:308–313, 2011), utilizing Banach’s fixed point theorem. This result remains valid under weaker assumptions through the product space approach. Moreover, we show that the stability analysis of the iterative algorithm proposed in their work (and in (J. Inequal. Appl. 2010:437976, 2010)) contains a flaw, which we address using Ostrowski’s classical result from 1967 (Z. Angew. Math. Mech. 47:77–81, 1967). Finally, we examine and improve the convergence theorem for solving a system of variational inequalities as established by Chang et al. (Appl. Math. Lett. 20:329–334, 2007).https://doi.org/10.1186/s13660-025-03252-3System of nonlinear equationsStability analysisProcedure schemeStrong monotonicityProduct space approach |
| spellingShingle | Satit Saejung On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme Journal of Inequalities and Applications System of nonlinear equations Stability analysis Procedure scheme Strong monotonicity Product space approach |
| title | On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme |
| title_full | On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme |
| title_fullStr | On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme |
| title_full_unstemmed | On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme |
| title_short | On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme |
| title_sort | on the existence of solutions of the system of nonlinear quasi mixed equilibrium problems and their stability of the procedure scheme |
| topic | System of nonlinear equations Stability analysis Procedure scheme Strong monotonicity Product space approach |
| url | https://doi.org/10.1186/s13660-025-03252-3 |
| work_keys_str_mv | AT satitsaejung ontheexistenceofsolutionsofthesystemofnonlinearquasimixedequilibriumproblemsandtheirstabilityoftheprocedurescheme |