On Mixed Equilibrium Problems in Hadamard Spaces
The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-con...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2019/3210649 |
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| _version_ | 1832554876617359360 |
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| author | Chinedu Izuchukwu Kazeem Olalekan Aremu Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo Safeer Hussain Khan |
| author_facet | Chinedu Izuchukwu Kazeem Olalekan Aremu Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo Safeer Hussain Khan |
| author_sort | Chinedu Izuchukwu |
| collection | DOAJ |
| description | The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature. |
| format | Article |
| id | doaj-art-18d9942b95154a59bf6ffdce3647600c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-18d9942b95154a59bf6ffdce3647600c2025-02-03T05:50:17ZengWileyJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/32106493210649On Mixed Equilibrium Problems in Hadamard SpacesChinedu Izuchukwu0Kazeem Olalekan Aremu1Olawale Kazeem Oyewole2Oluwatosin Temitope Mewomo3Safeer Hussain Khan4School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South AfricaDepartment of Mathematics, Statistics and Physics, Qatar University, Doha, QatarThe main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.http://dx.doi.org/10.1155/2019/3210649 |
| spellingShingle | Chinedu Izuchukwu Kazeem Olalekan Aremu Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo Safeer Hussain Khan On Mixed Equilibrium Problems in Hadamard Spaces Journal of Mathematics |
| title | On Mixed Equilibrium Problems in Hadamard Spaces |
| title_full | On Mixed Equilibrium Problems in Hadamard Spaces |
| title_fullStr | On Mixed Equilibrium Problems in Hadamard Spaces |
| title_full_unstemmed | On Mixed Equilibrium Problems in Hadamard Spaces |
| title_short | On Mixed Equilibrium Problems in Hadamard Spaces |
| title_sort | on mixed equilibrium problems in hadamard spaces |
| url | http://dx.doi.org/10.1155/2019/3210649 |
| work_keys_str_mv | AT chineduizuchukwu onmixedequilibriumproblemsinhadamardspaces AT kazeemolalekanaremu onmixedequilibriumproblemsinhadamardspaces AT olawalekazeemoyewole onmixedequilibriumproblemsinhadamardspaces AT oluwatosintemitopemewomo onmixedequilibriumproblemsinhadamardspaces AT safeerhussainkhan onmixedequilibriumproblemsinhadamardspaces |