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A necessary and sufficient condition for the strong convergence of Lipschitzian pseudocontractive mapping in Banach spaces

✍ Scribed by Yu-Chao Tang; Ji-Gen Peng; Liang-Gen Hu; Li-Wei Liu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
207 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

The purpose of this paper is to establish some necessary and sufficient conditions for the strong convergence of the Ishikawa iterative sequence and the Mann iterative sequence to a fixed point of pseudocontractive mapping in Banach spaces. Our results, to some extent, improve and extend the well-known result of [S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44(1) (1974) 147-150.] to Banach spaces.

πŸ“œ SIMILAR VOLUMES

Strong convergence of an explicit iterat
Strong convergence of an explicit iteration process for a totally asymptotically -nonexpansive mapping in Banach spaces
✍ Farrukh Mukhamedov; Mansoor Saburov πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 276 KB

In this work we prove the strong convergence of an explicit iterative process to a common fixed point of a totally asymptotically I-nonexpansive mapping T and a totally asymptotically nonexpansive mapping I, defined on a nonempty closed convex subset of a uniformly convex Banach space.