Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings

  • Kim, Tae-Hwa (Division of Mathematical Sciences, Pukyong National University) ;
  • Park, Yong-Kil (Department of Liberal Arts, Hanzhong University)
  • Received : 2009.09.25
  • Accepted : 2009.11.16
  • Published : 2009.12.31
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Abstract

In this paper, we first introduce a family S = {$S_n$ : C ${\rightarrow}$ C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {$x_n$} defined recursively by the algorithm $x_{n+1}$ = $S_nx_n$, $n{\geq}1$, starting from an initial guess $x_1{\in}C$, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added.

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References

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