Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 4,  2009, pp.701-712
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.4.701
Title & Authors
Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings
Kim, Tae-Hwa; Park, Yong-Kil;

Abstract
In this paper, we first introduce a family S = {$\small{S_n}$ : C $\small{{\rightarrow}}$ 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 {$\small{x_n}$} defined recursively by the algorithm $\small{x_{n+1}}$ = $\small{S_nx_n}$, $\small{n{\geq}1}$, starting from an initial guess $\small{x_1{\in}C}$, 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.
Keywords
Common fixed points;non-Lipschitzian mappings;total asymptotically nonexpansive mappings;strong convergence;
Language
English
Cited by
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