Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 831491, 7 pages.

On Cyclic Generalized Weakly C -Contractions on Partial Metric Spaces

Erdal Karapınar and Vladimir Rakocević

Full-text: Open access

Abstract

We give new results of a cyclic generalized weakly C -contraction in partial metric space. The results of this paper extend, generalize, and improve some fixed point theorems in the literature.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 831491, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807744

Digital Object Identifier
doi:10.1155/2013/831491

Mathematical Reviews number (MathSciNet)
MR3066315

Zentralblatt MATH identifier
1271.54081

Citation

Karapınar, Erdal; Rakocević, Vladimir. On Cyclic Generalized Weakly $C$ -Contractions on Partial Metric Spaces. J. Appl. Math. 2013, Special Issue (2013), Article ID 831491, 7 pages. doi:10.1155/2013/831491. https://projecteuclid.org/euclid.jam/1394807744


Export citation

References

  • S. G. Matthews, “Partial metric topology,” in Proceedings of the 8th Summer Conference on General Topology and Applications, vol. 728, pp. 183–197, Annals of the New York Academy of Sciences, 1994.
  • M. Bukatin, R. Kopperman, S. Matthews, and H. Pajoohesh, “Partial metric spaces,” American Mathematical Monthly, vol. 116, no. 8, pp. 708–718, 2009.
  • M. H. Escardó, “PCF extended with real numbers,” Theoretical Computer Science, vol. 162, no. 1, pp. 79–115, 1996.
  • R. Heckmann, “Approximation of metric spaces by partial metric spaces,” Applied Categorical Structures, vol. 7, no. 1-2, pp. 71–83, 1999.
  • R. D. Kopperman, S. G. Matthews, and H. Pajoohesh, “What do partial metrics represent?” in Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown, 2004.
  • P. Waszkiewicz, “Partial metrisability of continuous posets,” Mathematical Structures in Computer Science, vol. 16, no. 2, pp. 359–372, 2006.
  • M. Abbas, T. Nazir, and S. Romaguera, “Fixed point results for generalized cyclic contraction mappings in partial metric spaces,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales A, vol. 106, no. 2, pp. 287–297, 2012.
  • 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.
  • T. Abdeljawad, E. Karap\inar, and K. Taş, “A generalized contraction principle with control functions on partial metric spaces,” Computers & Mathematics with Applications, vol. 63, no. 3, pp. 716–719, 2012.
  • T. Abdeljawad, E. Karap\inar, and K. Taş, “Existence and uniqueness of a common fixed point on partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1900–1904, 2011.
  • R. P. Agarwal, M. A. Alghamdi, and N. Shahzad, “Fixed point theory for cyclic generalized contractions in partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 40, 2012.
  • 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, “Fixed point results for weakly contractive mappings in ordered partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, pp. 1–12, 2011.
  • H. Aydi, E. Karap\inar, and W. Shatanawi, “Coupled fixed point results for ($\psi $, $\varphi $)-weakly contractive condition in ordered partial metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4449–4460, 2011.
  • 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.
  • D. Ilić, V. Pavlović, and V. Rakočević, “Extensions of the Zamfirescu theorem to partial metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 801–809, 2012.
  • E. Karapinar and K. Sadarangani, “Fixed point theory for cyclic $(\varphi -\psi )$-contractions,” Fixed Point Theory and Applications, vol. 2011, article 69, 2011.
  • E. Karap\inar and. M. Erhan, “Fixed point theorems for operators on partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1894–1899, 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. Yuksel, “Some common fixed point theorems in PMS,” Journal of Applied Mathematics, vol. 2011, Article ID 263621, 16 pages, 2011.
  • E. Karapinar, “A note on common fixed point theorems in partial metric spaces,” Miskolc Mathematical Notes, vol. 12, no. 2, pp. 185–191, 2011.
  • S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 493298, 6 pages, 2010.
  • S. Romaguera and O. Valero, “A quantitative computational model for complete partial metric spaces via formal balls,” Mathematical Structures in Computer Science, vol. 19, no. 3, pp. 541–563, 2009.
  • H. K. Nashine, Z. Kadelburg, and S. Radenović, “Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces,” Mathematical and Computer Modelling, vol. 57, no. 9-10, pp. 2355–2365, 2013.
  • H. K. Nashine and Z. Kadelburg, “Cyclic contractions and fixed point results via control functions on partial metric spaces,” International Journal of Analysis, vol. 2013, Article ID 726387, 9 pages, 2013.
  • R. H. Haghi, Sh. Rezapour, and N. Shahzad, “Be careful on partial metric fixed point results,” Topology and its Applications, vol. 160, no. 3, pp. 450–454, 2013.
  • S. K. Chatterjea, “Fixed-point theorems,” Doklady Bolgarskoĭ Akademii Nauk. Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972.
  • B. S. Choudhury, “Unique fixed point theorem for weak \emphC-contractive mappings, Kathmandu University,” Journal of Science, Engineering and Technology, vol. 5, no. 1, pp. 6–13, 2009.
  • Ya. I. Alber and S. Guerre-Delabriere, “Principle of weakly contractive maps in Hilbert spaces,” in New Results in Operator Theory and Its Applications, vol. 98 of Operator Theory: Advances and Applications, pp. 7–22, Birkhäuser, Basel, Switzerland, 1997.
  • B. E. Rhoades, “Some theorems on weakly contractive maps,” Nonlinear Analysis. Theory, Methods & Applications, vol. 47, pp. 2683–2693, 2001.
  • W. A. Kirk, P. S. Srinivasan, and P. Veeramani, “Fixed points for mappings satisfying cyclical contractive conditions,” Fixed Point Theory, vol. 4, no. 1, pp. 79–89, 2003.
  • M. Păcurar and I. A. Rus, “Fixed point theory for cyclic $\phi $-contractions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1181–1187, 2010.
  • E. Karap\inar, “Fixed point theory for cyclic weak \emphC-contraction,” Applied Mathematics Letters, vol. 24, no. 6, pp. 822–825, 2011.
  • J. Harjani, B. López, and K. Sadarangani, “Fixed point theorems for weakly $C$-contractive mappings in ordered metric spaces,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 790–796, 2011.