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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 103764, 8 pages
http://dx.doi.org/10.1155/2014/103764
Research Article

Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

Department of Mathematics, Nanchang University, Nanchang 330031, China

Received 4 July 2014; Accepted 16 September 2014; Published 16 October 2014

Academic Editor: Simeon Reich

Copyright © 2014 Chuanxi Zhu et al. 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 introduce the concepts of -contraction and probabilistic -contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.