Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces
The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/5/722 |
| _version_ | 1811263340020760576 |
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| author | Mujahid Abbas Yusuf Ibrahim Abdul Rahim Khan Manuel de la Sen |
| author_facet | Mujahid Abbas Yusuf Ibrahim Abdul Rahim Khan Manuel de la Sen |
| author_sort | Mujahid Abbas |
| collection | DOAJ |
| description | The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result. |
| first_indexed | 2024-04-12T19:44:02Z |
| format | Article |
| id | doaj.art-3de361a9f074439f9b6b2715893529ce |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:44:02Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3de361a9f074439f9b6b2715893529ce2022-12-22T03:19:00ZengMDPI AGSymmetry2073-89942019-05-0111572210.3390/sym11050722sym11050722Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach SpacesMujahid Abbas0Yusuf Ibrahim1Abdul Rahim Khan2Manuel de la Sen3Department of Mathematics, Government College University, Katchery Road, Lahore 54000, PakistanDepartment of Mathematics, Sa’adatu Rimi College of Education, Kumbotso Kano, P.M.B. 3218 Kano, NigeriaDepartment of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaInstitute of Research and Development of Processes, University of The Basque Country, Campus of Leioa (Bizkaia), 48080 Leioa, SpainThe purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result.https://www.mdpi.com/2073-8994/11/5/722split variational inclusion problemgeneralized mixed equilibrium problemfixed point problemmaximal monotone operatorleft Bregman asymptotically nonexpansive mappinguniformly convex and uniformly smooth Banach space |
| spellingShingle | Mujahid Abbas Yusuf Ibrahim Abdul Rahim Khan Manuel de la Sen Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces Symmetry split variational inclusion problem generalized mixed equilibrium problem fixed point problem maximal monotone operator left Bregman asymptotically nonexpansive mapping uniformly convex and uniformly smooth Banach space |
| title | Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces |
| title_full | Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces |
| title_fullStr | Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces |
| title_full_unstemmed | Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces |
| title_short | Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces |
| title_sort | strong convergence of a system of generalized mixed equilibrium problem split variational inclusion problem and fixed point problem in banach spaces |
| topic | split variational inclusion problem generalized mixed equilibrium problem fixed point problem maximal monotone operator left Bregman asymptotically nonexpansive mapping uniformly convex and uniformly smooth Banach space |
| url | https://www.mdpi.com/2073-8994/11/5/722 |
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