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http://dx.doi.org/10.4134/BKMS.2013.50.3.1007

APPROXIMATING FIXED POINTS OF NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES WITHOUT UNIFORM CONVEXITY  

Sahu, Daya Ram (Department of Mathematics Banaras Hindu University)
Khan, Abdul Rahim (Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals)
Kang, Shin Min (Department of Mathematics and RINS Gyeongsang National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 1007-1020 More about this Journal
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 [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 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;
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