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In this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.
Wydawca
Czasopismo
Rocznik
Tom
Strony
382--395
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
autor
- School of Science, University of Phayao, Phayao 56000, Thailand
autor
- School of Science, University of Phayao, Phayao 56000, Thailand
autor
- Department of Mathematics, Faculty of Science Chiang Mai University, Chiang Mai 50200, Thailand
Bibliografia
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- [8] W. Cholamjiak, S. Suantai, A hybrid method for a countable family of multivalued maps, equilibrium problems, and variational inequality problems, Discrete Dyn. Nat. Soc. Volume 2010 (2010), Article ID 349158, 14 pages.
- [9] P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), 117–136.
- [10] H. He, S. Liu, Y. J. Cho, An explicit method for systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings, J. Comput. Appl. Math. 235 (2011), 4128–4139.
- [11] N. Hussain, A. R. Khan, Applications of the best approximation operator to *-nonexpansive maps in Hilbert spaces, Numer. Funct. Anal. Optim. 24 (2003), 327–338.
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- [13] P. Kumam, A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping, Nonlinear Anal.: Hybr. Syst. 2 (2008), 1245–1255.
- [14] P. Kumam, A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping, J. Appl. Math. Comput. 29 (2009), 263–280.
- [15] G. Marino, H. K. Xu, Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336–346.
- [16] A. Moudafi, Viscosity approximation methods for fixed-point problems, J. Math. Anal. Appl. 241 (2000), 46–55.
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- [25] Y. Shehu, A new hybrid iterative scheme for countable families of relatively quasinonexpansive mappings and system of equilibrium problems, Int. J. Math. Math. Sci. (2011), Art. ID 131890, 23 pages, 2011.
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- [32] H. Zegeye, N. Shahzad, Viscosity approximation methods for nonexpansive multimaps in Banach space, Acta Math. Sinica 26 (2010), 1165–1176.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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