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Abstract and Applied Analysis
Volume 2013, Article ID 381715, 9 pages
http://dx.doi.org/10.1155/2013/381715
Research Article

Some Convergence Theorems for Contractive Type Mappings in CAT(0) Spaces

Graduate School of Education, Mathematics Education, Kyungnam University, Changwon, Kyungnam 631-701, Republic of Korea

Received 9 September 2013; Accepted 22 October 2013

Academic Editor: Sehie Park

Copyright © 2013 Kyung Soo Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish theorems of strong convergence, for the Ishikawa-type (or two step; cf. Ishikawa, 1974) iteration scheme, to a fixed point of a uniformly L-Lipschitzian asymptotically demicontractive mapping and a uniformly L-Lipschitzian hemicontractive mapping in CAT(0) space. Moreover, we will propose some open problems.