Abstract and Applied Analysis
Volume 2011 (2011), Article ID 143959, 18 pages
http://dx.doi.org/10.1155/2011/143959
Research Article

Fixed Point Theorems for Nonlinear Contractions in Menger Spaces

Jeong Sheok Ume

Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

Received 14 May 2011; Accepted 24 June 2011

Academic Editor: H. B. Thompson

Copyright © 2011 Jeong Sheok Ume. 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

The main purpose of this paper is to introduce a new class of Ćirić-type contraction and to present some fixed point theorems for this mapping as well as for Caristi-type contraction. Several examples are given to show that our results are proper extension of many known results.