Table of Contents
Chinese Journal of Mathematics
Volume 2013 (2013), Article ID 859531, 8 pages
http://dx.doi.org/10.1155/2013/859531
Research Article

A Generalization of Prešić Type Mappings in 0-Complete Ordered Partial Metric Spaces

1Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli, Sanwer Road, Indore 453331, India
2Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia

Received 25 July 2013; Accepted 13 August 2013

Academic Editors: G. Liu and S. A. Marano

Copyright © 2013 Satish Shukla and Stojan Radenović. 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

  1. S. B. Prešić, “Sur la convergence des suites, Comptes,” Rendus de l'Académie de Paris, vol. 260, pp. 3828–3830, 1965. View at Google Scholar
  2. S. B. Prešić, “Sur une classe dinequations aux differences finite et sur la convergence de certaines suites,” Publications de l'Institut Mathématique, vol. 5, no. 19, pp. 75–78, 1965. View at Google Scholar
  3. Y. Z. Chen, “A Presic type contractive condition and its applications,” Nonlinear Analysis, vol. 71, no. 12, pp. e2012–e2017, 2009. View at Publisher · View at Google Scholar
  4. L. B. Ćirić and S. B. Prešić, “On Presic type generalisation of Banach contraction principle,” Acta Mathematica Universitatis Comenianae, vol. 2, pp. 143–147, 2007. View at Google Scholar
  5. R. George, K. P. Reshma, and R. Rajagopalan, “A generalised fixed point theorem of Presic type in cone metric spaces and application to Morkov process,” Fixed Point Theory and Applications, vol. 2011, article 85, 2011. View at Publisher · View at Google Scholar
  6. M. S. Khan, M. Berzig, and B. Samet, “Some convergence results for iterative sequences of Presic type and applications,” Advances in Difference Equations, vol. 2012, article 38, 2012. View at Publisher · View at Google Scholar
  7. S. K. Malhotra, S. Shukla, and R. Sen, “A generalization of Banach contraction principle in ordered cone metric spaces,” Journal of Advanced Mathematical Studies, vol. 5, no. 2, pp. 59–67, 2012. View at Google Scholar
  8. M. Pǎcurar, “A multi-step iterative method for approximating common fixed points of Prešić-Rus type operators on metric spaces,” Studia Universitatis Babes-Bolyai, Mathematica, vol. 55, no. 1, 2010. View at Google Scholar
  9. M. Pǎcurar, “Approximating common fixed points of Presić-Kannan type operators by a multi-step iterative method,” Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, vol. 17, no. 1, pp. 153–168, 2009. View at Google Scholar · View at Scopus
  10. M. Pǎcurar, “Common fixed points for almost presíc type operators,” Carpathian Journal of Mathematics, vol. 28, no. 1, pp. 117–126, 2012. View at Google Scholar · View at Scopus
  11. S. Shukla, R. Sen, and S. Radenovic, “Set-valued Presic type contraction in metric spaces,” Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică. In press.
  12. S. G. Matthews, “Partial metric topology,” in Proceedings of the 8th Summer Conference on General Topology and Application, vol. 728 of Annals of the New York Academy of Sciences, pp. 183–197, 1994.
  13. 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. View at Publisher · View at Google Scholar
  14. 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, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. 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. View at Publisher · View at Google Scholar
  16. H. Aydi, “Fixed point results for weakly contractive mappings in ordered partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, p. 112, 2011. View at Google Scholar
  17. H. Aydi, “Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces,” Nonlinear Analysis, vol. 2, no. 2, p. 3348, 2011. View at Google Scholar
  18. H. Aydi, “Some coupled fixed point results on partial metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, Article ID 647091, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Aydi, “Some fixed point results in ordered partial metric spaces,” The Journal of Nonlinear Science and Applications, vol. 4, no. 3, pp. 210–217, 2011. View at Google Scholar
  20. H. Aydi and E. Karapinar, “A Meir-Keeler common type fixed point theorem on partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 26, 2012. View at Publisher · View at Google Scholar
  21. L. Ćirić, B. Samet, H. Aydi, and C. Vetro, “Common fixed points of generalized contractions on partial metric spaces and an application,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2398–2406, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. R. Heckmann, “Approximation of metric spaces by partial metric spaces,” Applied Categorical Structures, vol. 7, no. 1-2, pp. 71–83, 1999. View at Google Scholar · View at Scopus
  23. D. Ilić, V. Pavlović, and V. Rakočević, “Some new extensions of Banachs contraction principle to partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1326–1330, 2011. View at Publisher · View at Google Scholar
  24. Z. Kadelburg, H. K. Nashine, and S. Radenovic, “Fixed point results under various contractive conditions in partial metric spaces,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales A, 2012. View at Publisher · View at Google Scholar
  25. E. Karapnar and U. Yüksel, “Some common fixed point theorems in partial metric spaces,” Journal of Applied Mathematics, vol. 2011, Article ID 263621, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Oltra, S. Romaguera, and E. A. Sánchez-Pérez, “Bicompleting weightable quasi-metric spaces and partial metric spaces,” Rendiconti del Circolo Matematico di Palermo, vol. 51, no. 1, pp. 151–162, 2002. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Radenovi and Z. Kadelburg, “Generalized weak contractions in partially ordered metric spaces,” Computers and Mathematics with Applications, vol. 60, no. 6, pp. 1776–1783, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. O. Valero, “On Banach fixed point theorems for partial metric spaces,” Applied General Topology, vol. 6, pp. 229–240, 2005. View at Google Scholar
  29. W. Shatanawi, B. Samet, and M. Abbas, “Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 680–687, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. 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. View at Publisher · View at Google Scholar
  31. I. Altun and S. Romaguera, “Characterization of partial metric completeness in terms of weakly contractive mapping having fixed point,” Applicable Analysis and Discrete Mathematics, vol. 6, no. 2, pp. 247–256, 2012. View at Publisher · View at Google Scholar
  32. S. Romaguera, “Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces,” Applied General Topology, vol. 12, no. 2, pp. 213–220, 2011. View at Google Scholar · View at Scopus
  33. 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 Scopus
  34. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at Scopus
  35. J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205–2212, 2007. View at Publisher · View at Google Scholar · View at Scopus
  36. N. V. Luong and N. X. Thuan, “Some fixed point theorems of Prešić-Ćirić type,” Acta Universitatis Apulensis, No. 30/2012, pp. 237-249.
  37. S. Oltra and O. Valero, “Banach’s fixed point theorems for metric spaces,” Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 36, pp. 17–26, 2004. View at Google Scholar
  38. S. J. O'Neill, “Partial metrics, valuations and domain theory,” in Proceedings of the11th Summer Conference on General Topology and Applications, vol. 806 of Annals of the New York Academy of Sciences, pp. 304–315, 1996.
  39. M. Abbas and G. Jungck, “Common fixed point results for noncommuting mappings without continuity in cone metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 416–420, 2008. View at Publisher · View at Google Scholar · View at Scopus