Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Remarks on Fixed Point Theorems of Non-Lipschitzian Self-mappings

  • Kim, Tae-Hwa (Division of Mathematical Sciences, Pukyong National University) ;
  • Jeon, Byung-Ik (Division of Mathematical Sciences, Pukyong National University)
  • Received : 2004.04.20
  • Published : 2005.09.23
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Abstract

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

Keywords

References

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