AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS
In this paper, we consider a general composite iterative algorithm for finding a common element of the set of solutions of a generalised mixed equilibrium problem, the set of fixed points of an infinite family of non-expansive mappings and the set of solutions of a variational inequality problem for...
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| Format: | Article |
| Language: | English |
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Dalat University
2012-06-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
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| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/201 |
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| author | Jong Soo Jung |
| author_facet | Jong Soo Jung |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | In this paper, we consider a general composite iterative algorithm for finding a common element of the set of solutions of a generalised mixed equilibrium problem, the set of fixed points of an infinite family of non-expansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimisation problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area. |
| format | Article |
| id | doaj-art-e506f81c140248c081e01cf887e6a885 |
| institution | Kabale University |
| issn | 0866-787X |
| language | English |
| publishDate | 2012-06-01 |
| publisher | Dalat University |
| record_format | Article |
| series | Tạp chí Khoa học Đại học Đà Lạt |
| spelling | doaj-art-e506f81c140248c081e01cf887e6a8852025-02-02T00:30:57ZengDalat UniversityTạp chí Khoa học Đại học Đà Lạt0866-787X2012-06-012210.37569/DalatUniversity.2.2.201(2012)AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMSJong Soo Jung0Department of Mathematics, Dong-A University, KoreaIn this paper, we consider a general composite iterative algorithm for finding a common element of the set of solutions of a generalised mixed equilibrium problem, the set of fixed points of an infinite family of non-expansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimisation problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area.https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/201Generalised mixed equilibrium problemFixed pointNon-expansive mappingInverse-strongly monotone mappingVariational inequalityOptimisation problem |
| spellingShingle | Jong Soo Jung AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS Tạp chí Khoa học Đại học Đà Lạt Generalised mixed equilibrium problem Fixed point Non-expansive mapping Inverse-strongly monotone mapping Variational inequality Optimisation problem |
| title | AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS |
| title_full | AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS |
| title_fullStr | AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS |
| title_full_unstemmed | AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS |
| title_short | AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS |
| title_sort | iterative algorithm for generalised mixed equilibrium problems variational inequality problems and optimisation problems |
| topic | Generalised mixed equilibrium problem Fixed point Non-expansive mapping Inverse-strongly monotone mapping Variational inequality Optimisation problem |
| url | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/201 |
| work_keys_str_mv | AT jongsoojung aniterativealgorithmforgeneralisedmixedequilibriumproblemsvariationalinequalityproblemsandoptimisationproblems AT jongsoojung iterativealgorithmforgeneralisedmixedequilibriumproblemsvariationalinequalityproblemsandoptimisationproblems |