Abstract and Applied Analysis

Common Fixed Point Results for Four Mappings on Partial Metric Spaces

A. Duran Turkoglu and Vildan Ozturk

Full-text: Open access

Abstract

We give fixed point results for four mappings which satisfy almost generalized contractive condition on partial metric space and we support the results with an example.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 190862, 11 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475862

Digital Object Identifier
doi:10.1155/2012/190862

Mathematical Reviews number (MathSciNet)
MR2984025

Zentralblatt MATH identifier
1253.54054

Citation

Turkoglu, A. Duran; Ozturk, Vildan. Common Fixed Point Results for Four Mappings on Partial Metric Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 190862, 11 pages. doi:10.1155/2012/190862. https://projecteuclid.org/euclid.aaa/1364475862


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References

  • S. G. Matthews, “Partial Metric topology,” in Proceedings of the 8th Summer Conference at Queens College, S. Andima, Ed., vol. 728 of Papers on General Topology and Applications, Annals of the New York Academy of Sciences, pp. 183–197, 1992.
  • S. G. Matthews, “Partial metric topology,” Research Report 212, Department of Computer Science, University of Warwick, 1992.
  • T. Abdeljawad, “Fixed points for generalized weakly contractive mappings in partial metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2923–2927, 2011.
  • I. Altun and A. Erduran, “Fixed point theorems for monotone mappings on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 508730, 10 pages, 2011.
  • I. Altun, F. Sola, and H. Simsek, “Generalized contractions on partial metric spaces,” Topology and Its Applications, vol. 157, no. 18, pp. 2778–2785, 2010.
  • H. Aydi and and E. Karapinar, “A Meir-Keeler common type fixed point theo-rem on partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, Article ID 26, 10 pages, 2012.
  • L. Ćirić, M. Abbas, R. Saadati, and N. Hussain, “Common fixed points of almost generalized contractive mappings in ordered metric spaces,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5784–5789, 2011.
  • K. P. Chi, E. Karapinar, and T. D. Thanh, “A generalized contraction prin-ciple in partial metric spaces,” Mathematical and Computer Modelling, vol. 55, pp. 1673–1681, 2012.
  • D. Ilić, V. Pavlović, and V. Rakočević, “Some new extensions of Banach's contraction principle to partial metric space,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1326–1330, 2011.
  • E. Karapinar, “Generalizations of Caristi Kirk's theorem on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 4, 2011.
  • E. Karap\inar and U. Yüksel, “Some common fixed point theorems in partial metric spaces,” Journal of Applied Mathematics, vol. 2011, Article ID 263621, 16 pages, 2011.
  • S. Oltra and O. Valero, “Banach's fixed point theorem for partial metric spaces,” Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 36, no. 1-2, pp. 17–26, 2004.
  • S. Romaguera, “Fixed point theorems for generalized contractions on partial metric spaces,” Topology and Its Applications, vol. 159, no. 1, pp. 194–199, 2012.
  • I. A. Rus, “Fixed point theory in partial metric spaces,” Analele Universitattii de Vest, Timitsoara, vol. 46, no. 2, pp. 149–160, 2008.
  • O. Valero, “On Banach fixed point theorems for partial metric spaces,” Applied General Topology, vol. 6, no. 2, pp. 229–240, 2005.
  • R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968.
  • S. Sessa, “On a weak commutativity condition of mappings in fixed point considerations,” Institut Mathématique. Publications, vol. 32, no. 46, pp. 149–153, 1982.
  • G. Jungck, “Common fixed points for commuting and compatible maps on compacta,” Proceedings of the American Mathematical Society, vol. 103, no. 3, pp. 977–983, 1988.
  • G. Jungck, “Common fixed points for noncontinuous nonself maps on nonmetric spaces,” Far East Journal of Mathematical Sciences, vol. 4, no. 2, pp. 199–215, 1996.
  • V. Berinde, “Approximating fixed points of weak contractions using the Picard iteration,” Nonlinear Analysis, vol. 9, no. 1, pp. 43–53, 2004.
  • V. Berinde, “General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces,” Carpathian Journal of Mathematics, vol. 24, no. 2, pp. 10–19, 2008.
  • V. Berinde and M. Păcurar, “Fixed points and continuity of almost contractions,” Fixed Point Theory, vol. 9, no. 1, pp. 23–34, 2008.
  • G. V. R. Babu, M. L. Sandhya, and M. V. R. Kameswari, “A note on a fixed point theorem of Berinde on weak contractions,” Carpathian Journal of Mathematics, vol. 24, no. 1, pp. 8–12, 2008.
  • M. Abbas and D. Ilić, “Common fixed points of generalized almost nonexpansive mappings,” Filomat, vol. 24, no. 3, pp. 11–18, 2010.
  • I. Altun and O. Acar, “Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces,” Topology and Its Applications, vol. 159, no. 10-11, pp. 2642–2648, 2012.
  • A. Aghajani, S. Radenović, and J. R. Roshan, “Common fixed point results for four mappings satisfying almost generalized (S,T)-contractive condition in partially ordered metric spaces,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5665–5670, 2012.