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Abstract and Applied Analysis

Volume 2013 (2013), Article ID 312479, 10 pages

http://dx.doi.org/10.1155/2013/312479

## Berinde-Type Generalized Contractions on Partial Metric Spaces

^{1}Department of Mathematics, College of Education of Jubail, Dammam University, Saudi Arabia^{2}Laboratoire Physique Mathmaétique, Fonctions Spéciales et Applications (MAPSFA) LR11ES35, Université de Sousse, Ecole Supérieure des Sciences et de Technologie de Hammam Sousse, Rue Lamine el Abbassi, 4011 Hammam Sousse, Tunisia^{3}Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey

Received 21 October 2012; Accepted 4 December 2012

Academic Editor: Abdul Latif

Copyright © 2013 Hassen Aydi 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. G. Matthews, “Partial metric topology,” in
*Papers on General Topology and Applications*, vol. 728 of*Annals of the New York Academy of Sciences*, pp. 183–197, New York Academy of Sciences, New York, NY, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet - S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,”
*Fundamenta Mathematicae*, vol. 3, pp. 133–181, 1922. View at Google Scholar - T. Abedeljawad, E. Karapınar, and K. Taş, “Existence and uniqueness of common fixed point on partial metric spaces,”
*Applied Mathematics Letters*, vol. 24, pp. 1894–1899, 2011. View at Google Scholar - 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 · View at Zentralblatt MATH · View at MathSciNet - I. Altun and A. Erduran, “Fixed point theorems for monotone mappings on partial metric spaces,”
*Fixed Point Theory and Applications*, Article ID 508730, 10 pages, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. Aydi, “Some coupled fixed point results on partial metric spaces,”
*International Journal of Mathematics and Mathematical Sciences*, Article ID 647091, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. Aydi, “Some fixed point results in ordered partial metric spaces,”
*Journal of Nonlinear Science and Its Applications*, vol. 4, no. 3, pp. 210–217, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Google Scholar · View at MathSciNet - H. Aydi, “Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces,”
*Journal of Nonlinear Analysis and Optimization*, vol. 2, no. 2, pp. 269–284, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - H. Aydi, “Common fixed point results for mappings satisfying ($\psi ,\varphi $)-weak contractions in ordered partial metric spaces,”
*International Journal of Mathematics and Statistics*, no. 2, pp. 53–64, 2012. View at Google Scholar · View at MathSciNet - H. Aydi, “Coupled fixed point results in ordered partial metric spaces,”
*Selçuk Journal of Applied Mathematics*, vol. 13, no. 1, pp. 23–33, 2012. View at Google Scholar - 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 Zentralblatt MATH · View at MathSciNet - C. Di Bari, M. Milojević, S. Radenović, and P. Vetro, “Common fixed points for self-mappings on partial metric spaces,”
*Fixed Point Theory and Applications*. Preprint. - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. Abdeljawad, E. Karapınar, 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. View at Publisher · View at Google Scholar · View at MathSciNet - E. Karapınar, “A note on common fixed point theorems in partial metric spaces,”
*Miskolc Mathematical Notes*, vol. 12, no. 2, pp. 185–191, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - E. Karapınar, “Some fixed point theorems on the class of comparable partial metric spaces,”
*Applied General Topology*, vol. 12, no. 2, pp. 187–192, 2011. View at Google Scholar · View at MathSciNet - E. Karapınar, “Generalizations of Caristi Kirk's theorem on partial metric spaces,”
*Fixed Point Theory and Applications*, vol. 4, 7 pages, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - E. Karapınar, “Ćirić types nonunique fixed point theorems on partial metric spaces,”
*Journal of Nonlinear Science and Its Applications*, vol. 5, no. 2, pp. 74–83, 2012. View at Google Scholar · View at MathSciNet - E. Karapınar, N. Shobkolaei, S. Sedghi, and S. M. Vaezpour, “A common fixed point theorem for cyclic operators on partial metric spaces,”
*Filomat*, vol. 26, pp. 407–414, 2012. View at Google Scholar - E. Karapınar, “Weak $\varphi $-contraction on partial metric spaces,”
*Journal of Computational Analysis and Applications*, vol. 14, no. 2, pp. 206–210, 2012. View at Publisher · View at Google Scholar · View at MathSciNet - S. Romaguera, “Fixed point theorems for generalized contractions on partial metric spaces,”
*Topology and Its Applications*, vol. 159, no. 1, pp. 194–199, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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 Zentralblatt MATH · View at MathSciNet - S. Romaguera and M. Schellekens, “Partial metric monoids and semivaluation spaces,”
*Topology and Its Applications*, vol. 153, no. 5-6, pp. 948–962, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - N. Shobkolaei, S. M. Vaezpour, and S. Sedghi, “A common fixed point theorem on ordered partial metric spaces,”
*Journal of Basic and Applied Scientific Research*, vol. 1, pp. 3433–3439, 2011. View at Google Scholar - A. D. T. Turkoglu and V. Ozturk, “Common fixed point results for four mappings on partial metric spaces,”
*Abstract and Applied Analysis*, vol. 2012, Article ID 190862, 11 pages, 2012. View at Publisher · View at Google Scholar - F. Vetro and S. Radenović, “Nonlinear $\psi $-quasi-contractions of Ćirić-type in partial metric spaces,”
*Applied Mathematics and Computation*, vol. 219, no. 4, pp. 1594–1600, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - V. Berinde, “Approximating fixed points of weak contractions using the Picard iteration,”
*Nonlinear Analysis Forum*, vol. 9, no. 1, pp. 43–53, 2004. View at Google Scholar · View at MathSciNet - 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. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Abbas and D. Ilić, “Common fixed points of generalized almost nonexpansive mappings,”
*Filomat*, vol. 24, no. 3, pp. 11–18, 2010. View at Publisher · View at Google Scholar · View at MathSciNet - V. Berinde, “Some remarks on a fixed point theorem for Ćirić-type almost contractions,”
*Carpathian Journal of Mathematics*, vol. 25, no. 2, pp. 157–162, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - V. Berinde, “Approximating common fixed points of noncommuting almost contractions in metric spaces,”
*Fixed Point Theory*, vol. 11, no. 2, pp. 179–188, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - V. Berinde, “Common fixed points of noncommuting almost contractions in cone metric spaces,”
*Mathematical Communications*, vol. 15, no. 1, pp. 229–241, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar - L. 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