Abstract
Some common fixed point results for generalized contractive mappings satisfying rational type expressions in the framework of partially ordered metric spaces are obtained. The results proved generalize and extend some known results in the literature.
Similar content being viewed by others
References
Agarwal, R.P., El-Gebeily, M.A., O’Regan, D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 109–116 (2008)
Bhaskar, T.G., Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379–1393 (2006)
Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531–536 (2002)
Chandok, S.: Some common fixed point theorems for generalized f-weakly contractive mappings. J. Appl. Math. Inform. 29, 257–265 (2011)
Chandok, S.: Some common fixed point theorems for generalized nonlinear contractive mappings. Comput. Math. Appl. 62, 3692–3699 (2011). doi:10.1016/j.camwa.2011.09.009
Chandok, S.: Common fixed points, invariant approximation and generalized weak contractions. Int. J. Math. Math. Sci. 2012, 102980 (2012). 11 pp.
Chandok, S.: Common fixed points for generalized nonlinear contractive mappings in metric spaces. Mat. Vesn. 65, 29–34 (2013)
Chandok, S.: Some common fixed point results for generalized weak contractive mappings in partially ordered metric spaces. J. Nonlinear Anal. Optim. (2013)
Chandok, S.: Common fixed point theorems for generalized contractions mappings. Thai J. Math. (accepted)
Chandok, S.: Coupled common fixed point theorems for a contractive condition of rational type in ordered metric spaces. J. Appl. Math. Inform. (accepted)
Chandok, S., Karapinar, E.: Some common fixed point results for generalized rational type weak contraction mappings in partially ordered metric spaces. Thai J. Math. 11, 251–260 (2013)
Chandok, S., Khan, M.S., Rao, K.P.R.: Some coupled common fixed point theorems for a pair of mappings satisfying a contractive condition of rational type. J. Nonlinear Anal. Appl. 2013, Jnaa-00174 (2013). 6 pp.
Chandok, S., Kim, J.K.: Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions. J. Nonlinear Funct. Anal. Appl. 17, 301–306 (2012)
Chandok, S., Mustafa, Z., Postolache, M.: Coupled common fixed point theorems for mixed g-monotone mappings in partially ordered G-metric spaces. Univ. Politeh. Sci. Bull., Ser. A: Appl. Math. Phys. (accepted)
Harjani, J., López, B., Sadarangani, K.: A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space. Abstr. Appl. Anal. 2010, 190701 (2010). 8 pp.
Jaggi, D.S.: Some unique fixed point theorems. Indian J. Pure Appl. Math. 8, 223–230 (1977)
Nieto, J.J., Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)
Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)
Acknowledgements
The authors are thankful to the learned referees for very valuable suggestions leading to an improvement of the paper.
The research work of the second author is supported by University Grants Commission, India (F.No. 39-48/2010(SR)).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chandok, S., Narang, T.D. & Taoudi, MA. Some Common Fixed Point Results in Partially Ordered Metric Spaces for Generalized Rational Type Contraction Mappings. Viet J Math 41, 323–331 (2013). https://doi.org/10.1007/s10013-013-0024-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10013-013-0024-4
Keywords
- Common fixed point
- Rational type contraction mappings
- Compatible mappings
- Weakly compatible mappings
- Ordered metric spaces