Abstract and Applied Analysis
Volume 2014 (2014), Article ID 979170, 7 pages
http://dx.doi.org/10.1155/2014/979170
Research Article
A Note on Best Approximation in 0-Complete Partial Metric Spaces
1Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo, Italy
2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Received 23 May 2014; Accepted 28 August 2014; Published 23 October 2014
Academic Editor: Erdal Karapınar
Copyright © 2014 Marta Demma 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
- E. Karapınar, “Fixed point theory for cyclic weak -contraction,” Applied Mathematics Letters, vol. 24, no. 6, pp. 822–825, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
- 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. View at Google Scholar · View at MathSciNet
- A. A. Eldred and P. Veeramani, “Existence and convergence of best proximity points,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1001–1006, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- M. de la Sen and E. Karapinar, “Best proximity points of generalized semicyclic impulsive self-mappings: applications to impulsive differential and difference equations,” Abstract and Applied Analysis, vol. 2013, Article ID 505487, 16 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
- M. Jleli, E. Karapınar, and B. Samet, “A short note on the equivalence between “best proximity” points and “fixed point” results,” Journal of Inequalities and Applications, vol. 2014, article 246, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
- E. Karapınar, “Best proximity points of cyclic mappings,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1761–1766, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- E. Karapınar, “On best proximity point of -Geraghty contractions,” Fixed Point Theory and Applications, vol. 2013, article 200, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
- 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, New York, NY, USA, 1994.
- M. Bukatin, R. Kopperman, S. G. Matthews, and H. Pajoohesh, “Partial metric spaces,” American Mathematical Monthly, vol. 116, no. 8, pp. 708–718, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- 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, vol. 106, no. 2, pp. 287–297, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- J. Ahmad, C. Di Bari, Y. J. Cho, and M. Arshad, “Some fixed point results for multi-valued mappings in partial metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 175, 2013. View at Publisher · View at Google Scholar · 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 Zentralblatt MATH · View at MathSciNet
- H. Aydi, “Common fixed points for four maps in ordered partial metric spaces,” Fasciculi Mathematici, no. 49, pp. 15–31, 2012. View at Google Scholar · View at MathSciNet
- H. Aydi, M. Abbas, and C. Vetro, “Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces,” Topology and its Applications, vol. 159, no. 14, pp. 3234–3242, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- C. Di Bari and P. Vetro, “Common fixed points for -contractions on partial metric spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 6, pp. 591–598, 2013. View at Google Scholar · View at MathSciNet
- E. Karapinar, “Weak -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 · View at Scopus
- D. Paesano and P. Vetro, “Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces,” Topology and its Applications, vol. 159, no. 3, pp. 911–920, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- F. Vetro and S. Radenović, “Nonlinear -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 MathSciNet · View at Scopus
- S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 493298, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
- C. di Bari, Z. Kadelburg, H. K. Nashine, and S. Radenović, “Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 113, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- H. K. Nashine, Z. Kadelburg, S. Radenović, and J. K. Kim, “Fixed point theorems under Hardy-Rogers contractive conditions on 0-complete ordered partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 180, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
- R. H. Haghi, S. Rezapour, and N. Shahzad, “Be careful on partial metric fixed point results,” Topology and its Applications, vol. 160, no. 3, pp. 450–454, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- M. Jleli, E. Karapınar, and B. Samet, “Further remarks on fixed-point theorems in the context of partial metric spaces,” Abstract and Applied Analysis, vol. 2013, Article ID 715456, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
- B. Samet, C. Vetro, and F. Vetro, “From metric spaces to partial metric spaces,” Fixed Point Theory and Applications, vol. 2013, article 5, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- T. Suzuki, M. Kikkawa, and C. Vetro, “The existence of best proximity points in metric spaces with the property UC,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2918–2926, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- C. Di Bari, T. Suzuki, and C. Vetro, “Best proximity points for cyclic Meir-Keeler contractions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 3790–3794, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- 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 · View at Scopus
- P. Hitzler and A. Seda, Mathematical Aspects of Logic Programming Semantics, Chapman & Hall/CRC Studies in Informatic Series, CRC Press, New York, NY, USA, 2011.
- P. V. Subrahmanyam, “Remarks on some fixed-point theorems related to Banach's contraction principle,” Journal of Mathematical and Physical Sciences, vol. 8, pp. 445–457, 1974. View at Google Scholar · View at MathSciNet
- J. Caballero, J. Harjani, and K. Sadarangani, “A best proximity point theorem for Geraghty-contractions,” Fixed Point Theory and Applications, vol. 2012, article 231, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
- M. Gabeleh and N. Shahzad, “Existence and uniqueness of a solution for some nonlinear programming problems,” Mediterranean Journal of Mathematics, 2014. View at Publisher · View at Google Scholar