Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.06.05
  • Published : 2013.05.31
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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.

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References

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