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

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.
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.