Hybrid algorithm for an \(\alpha\)-nonexpansive mapping in a Banach space
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Authors
Zi-Ming Wang
- Department of Foundation, Shandong Yingcai University, Jinan 250104, P. R. China.
Yongfu Su
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China.
Jinlong Kang
- Department of Foundation, Xi'an Communication of Institute, Xi'an 710106, P. R. China.
Abstract
In this paper, we prove strong convergence theorem by the hybrid method for an \(\alpha\)-nonexpansive mapping
in a Banach space. Our results complement and enrich the research contents of \(\alpha\)-nonexpansive mapping.
Simultaneously, our main result generalizes Takahashi, Takeuchi, Kubota's result[W. Takahashi, Y. Takeuchi
, R. Kubota, J. Math. Anal. Appl. 341 (2008) 276-286].
Share and Cite
ISRP Style
Zi-Ming Wang, Yongfu Su, Jinlong Kang, Hybrid algorithm for an \(\alpha\)-nonexpansive mapping in a Banach space, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 1, 56--63
AMA Style
Wang Zi-Ming, Su Yongfu, Kang Jinlong, Hybrid algorithm for an \(\alpha\)-nonexpansive mapping in a Banach space. J. Nonlinear Sci. Appl. (2012); 5(1):56--63
Chicago/Turabian Style
Wang, Zi-Ming, Su, Yongfu, Kang, Jinlong. "Hybrid algorithm for an \(\alpha\)-nonexpansive mapping in a Banach space." Journal of Nonlinear Sciences and Applications, 5, no. 1 (2012): 56--63
Keywords
- \(\alpha\)-nonexpansive mapping
- \(\alpha\)-mean-asymptotically-nonexpansive mapping
- Hybrid algorithm
- Fixed point
- Banach space.
MSC
References
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W. Takahashi, Y. Takeuchi, R. Kubota , Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. , 341 (2008), 276-286.