Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces
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Authors
Chakkrid Klin-eam
- Department of Mathematics, Faculty of Science, Naresuan University, , Thailand., Phitsanulok, 65000, Thailand.
- Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand.
Prondanai Kaskasem
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand.
Suthep Suantai
- Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand.
Abstract
We introduce a hybrid method for finding a common element of the set of solutions of an equilibrium
problem defined on the dual space of a Banach space and the set of common fixed points of a family
of generalized nonexpansive mappings and prove strong convergence theorems by using the new hybrid
method. Using our main results, we obtain some new strong convergence theorems for finding a solution
of an equilibrium problem and a fixed point of a family of generalized nonexpansive mappings in a Banach
space.
Share and Cite
ISRP Style
Chakkrid Klin-eam, Prondanai Kaskasem, Suthep Suantai, Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 7, 4963--4975
AMA Style
Klin-eam Chakkrid, Kaskasem Prondanai, Suantai Suthep, Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces. J. Nonlinear Sci. Appl. (2016); 9(7):4963--4975
Chicago/Turabian Style
Klin-eam, Chakkrid, Kaskasem, Prondanai, Suantai, Suthep. "Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces." Journal of Nonlinear Sciences and Applications, 9, no. 7 (2016): 4963--4975
Keywords
- Hybrid method
- generalized nonexpansive mapping
- NST-condition
- equilibrium problem
- fixed point problem
- Banach space.
MSC
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