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On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces -by Prondanai Kaskasem, Chakkrid Klin-eam and Suthep Suantai

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Abstract: In this paper, we prove some fixed point theorems of $\alpha$-nonexpansive mapping in Banach spaces which introduced by K. Goebel and M. A. Pineda (2007) [1]. In the first theorem of main result, we prove the existence of common fixed point sets of $\alpha$-nonexpansive mapping and continuous mapping. In the second theorem in our result, we confirm the existence of common fixed point sets of $\alpha$-nonexpansive mapping
and a mapping which it is either nonexpansive or weakly continuous. Moreover, we obtain that collection of $\alpha$-nonexpansive mapping has intersection property.

Keywords: Banach spaces, Fixed point, $\alpha$-nonexpansive mappings and Strictly convexity.

DOI: https://doi.org/10.30697/rfpta-2018-34

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How to cite this article: Prondanai Kaskasem, Chakkrid Klin-eam and Suthep Suantai, On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces, Results in Fixed Point Theory and Applications, vol. 2018, Article ID 201834, 6 pages, 2018.

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Copyright © 2018 SUMA Publishing Group., This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.