Abstract
Our purpose in this paper is to prove strong convergence theorems by hybrid methods for nonexpansive mappings in a Banach space under appropriate conditions. We first prove a strong convergence theorem by the shrinking projection method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. Next, we obtain another strong convergence theorem by the monotone hybrid method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. These theorems are proved by using the concept of set convergence.
Received: January 11, 2010
Revised: July 9, 2010
JEL classification: C62, C68
Mathematics Subject Classification (2000): 47H05, 47H09, 47H20
The research of the first author and the second author was partially supported by Grant-in-Aid for Scientific Research No. 19540167 from Japan Society for the Promotion of Science and by the grant NSC 98-2115-M-110-001, respectively.
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Takahashi, W., Yao, JC. (2011). Strong convergence theorems by hybrid methods for nonexpansive mappings with equilibrium problems in Banach spaces equilibrium problems in Banach spaces. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53883-7_9
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DOI: https://doi.org/10.1007/978-4-431-53883-7_9
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