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Abstract and Applied Analysis
Volume 2014, Article ID 581267, 9 pages
Research Article

New Results and Generalizations for Approximate Fixed Point Property and Their Applications

1Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan
2Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran
3School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5746, Tehran, Iran

Received 1 December 2013; Accepted 3 January 2014; Published 4 March 2014

Academic Editor: Erdal Karapınar

Copyright © 2014 Wei-Shih Du and Farshid Khojasteh. 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.


We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions and -admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.