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Journal of Mathematics
Volume 2013, Article ID 967045, 5 pages
http://dx.doi.org/10.1155/2013/967045
Research Article

Weak Contraction Condition Involving Cubic Terms of under the Fixed Point Consideration

Department of Pure and Applied Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, Chhattisgrah 495009, India

Received 31 January 2013; Accepted 14 April 2013

Academic Editor: Krassimir T. Atanassov

Copyright © 2013 Penumurthy Parvateesam Murthy and K. N. V. V. Vara Prasad. 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

A fixed point theorem is presented for single-valued map with using generalized -weak contractive condition involving various combinations of on a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008).