Journal of Operators

Volume 2013, Article ID 404573, 8 pages

http://dx.doi.org/10.1155/2013/404573

Research Article

## A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces

^{1}Department of Mathematics, Andhra University, Visakhapatnam 530 003, India^{2}Department of Mathematics, Lendi Institute of Engineering and Technology, Vizianagaram 535 005, India^{3}Department of Mathematics, Jimma University, Jimma-378, Ethiopia

Received 14 June 2013; Revised 30 October 2013; Accepted 2 November 2013

Academic Editor: Ram U. Verma

Copyright © 2013 G. V. R. Babu 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.

#### Linked References

- S. Banach, “Sur les operations dans les ensembles abstraits at leur application aux equaltions integrales,”
*Fundamenta Mathematicae*, vol. 3, pp. 173–181, 1922. View at Google Scholar - V. Berinde and F. Vetro, “Common fixed points of mappings satisfying implicit contractive conditions,”
*Fixed Point Theory and Applications*, vol. 2012, article 105, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. K. Chatterjea, “Fixed-point theorems,”
*Comptes Rendus de l'Académie Bulgare des Sciences*, vol. 25, pp. 727–730, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - L. B. Ćirić, “A generalization of Banach's contraction principle,”
*Proceedings of the American Mathematical Society*, vol. 45, pp. 267–273, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. Kannan, “Some results on fixed points,”
*Bulletin of the Calcutta Mathematical Society*, vol. 60, pp. 71–76, 1960. View at Google Scholar - R. Kannan, “Some results on fixed points-II,”
*The American Mathematical Monthly*, vol. 76, pp. 405–408, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Reich, “Kannan's fixed point theorem,”
*Bollettino della Unione Matematica Italiana*, vol. 4, no. 4, pp. 1–11, 1971. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - B. Samet, C. Vetro, and F. Vetro, “From metric spaces to partial metric spaces,”
*Fixed Point Theory and Applications*, vol. 2013, article 5, 2013. View at Google Scholar - A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,”
*Proceedings of the American Mathematical Society*, vol. 132, no. 5, pp. 1435–1443, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - D. Türkoğlu, O. Özer, and B. Fisher, “Fixed point theorems for $T$-orbitally complete spaces,”
*Mathematica*, no. 9, pp. 211–218, 1999. View at Google Scholar · View at MathSciNet - H.-S. Ding, Z. Kadelburg, and H. K. Nashine, “Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces,”
*Fixed Point Theory and Applications*, vol. 2012, article 85, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. K. Nashine, Z. Kadelburg, and Z. Golubović, “Common fixed point results using generalized altering distances on orbitally complete ordered metric spaces,”
*Journal of Applied Mathematics*, vol. 2012, Article ID 382094, 12 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. V. R. Babu and P. D. Sailaja, “A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces,”
*Thai Journal of Mathematics*, vol. 9, no. 1, pp. 1–10, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet