Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings |
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Authors: | Yongfu Su Ziming Wang Hongkun Xu |
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Affiliation: | aDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;bDepartment of Applied Mathematics, National Sun Yat-sen University, Taiwan |
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Abstract: | The purpose of this article is to prove strong convergence theorems for common fixed points of two closed hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Finally, a new simplified hybrid algorithm has been proposed and relative convergence theorem has been proved by using the new method for proofs. The results of this article modify and improve the results of Matsushita, Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257–266] and the results of Plubtieng, Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103–115], and many others. |
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Keywords: | Relatively nonexpansive mapping Hemi-relatively nonexpansive mapping Generalized projection Common fixed point Monotone hybrid algorithm |
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