Approximating fixed points of nonexpansive type mappings in Banach spaces without uniform convexity
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 1007-1020
https://doi.org/10.4134/BKMS.2013.50.3.1007
Printed May 31, 2013
Daya Ram Sahu, Abdul Rahim Khan, and Shin Min Kang
Banaras Hindu University, King Fahd University of Petroleum and Minerals, Gyeongsang National University
Abstract : Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [{\it Fixed points and iteration of a nonexpansive mapping in a Banach space}, Proc. Amer. Math. Soc. {\bf 59} (1976), 65--71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.
Keywords : nearly asymptotically nonexpansive mapping, asymptotically nonexpansive mapping, Mann iteration, nearly uniform $k$-contraction mapping, Opial condition
MSC numbers : 47H09, 47H10
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