A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces
We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi- ϕ -nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish...
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| Vydáno v: | Nonlinear analysis. Hybrid systems Ročník 4; číslo 4; s. 631 - 643 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.11.2010
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| ISSN: | 1751-570X |
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| Abstract | We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi-
ϕ
-nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish strong convergence theorems for this algorithm which are connected with results by Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Analysis 70 (2009) 45–57], Qin et al. [X. Qin, Y.J. Cho, S.M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20–30], Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Analysis: Hybrid Systems 3 (2009) 11–20], and many others. |
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| AbstractList | We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi-
ϕ
-nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish strong convergence theorems for this algorithm which are connected with results by Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Analysis 70 (2009) 45–57], Qin et al. [X. Qin, Y.J. Cho, S.M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20–30], Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Analysis: Hybrid Systems 3 (2009) 11–20], and many others. We introduce a hybrid projection iterative scheme for approximating a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of two quasi-[inline image]-nonexpansive mappings in a real uniformly convex and uniformly smooth Banach space. Then, we establish strong convergence theorems for this algorithm which are connected with results by Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Analysis 70 (2009) 45-57], Qin et al. [X. Qin, Y.J. Cho, S.M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225 (2009) 20-30], Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problems and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Analysis: Hybrid Systems 3 (2009) 11-20], and many others. |
| Author | Petrot, Narin Wattanawitoon, Kriengsak Kumam, Poom |
| Author_xml | – sequence: 1 givenname: Narin surname: Petrot fullname: Petrot, Narin email: narinp@nu.ac.th organization: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand – sequence: 2 givenname: Kriengsak surname: Wattanawitoon fullname: Wattanawitoon, Kriengsak email: s9510105@st.kmutt.ac.th organization: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thungkru, Bangkok 10140, Thailand – sequence: 3 givenname: Poom surname: Kumam fullname: Kumam, Poom email: poom.kum@kmutt.ac.th organization: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thungkru, Bangkok 10140, Thailand |
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| Keywords | Strong convergence Hybrid projection iterative scheme Generalized mixed equilibrium problem Quasi- ϕ -nonexpansive mapping Relatively nonexpansive mapping |
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| SubjectTerms | Algorithms Banach space Convergence Fixed points (mathematics) Generalized mixed equilibrium problem Hybrid projection iterative scheme Hybrid systems Mapping Nonlinearity Projection Quasi- [formula omitted]-nonexpansive mapping Relatively nonexpansive mapping Strong convergence Theorems |
| Title | A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces |
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