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;

Kim, Tae-Hwa; Park, Yong-Kil;

Abstract

In this paper, we first introduce a family S = { : C 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 {} defined recursively by the algorithm = , , starting from an initial guess , 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

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