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Annals of the Alexandru Ioan Cuza University - Mathematics

The Journal of "Alexandru Ioan Cuza" University from Iasi

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COMMON FIXED POINT OF MAPS IN COMPLETE PARTIAL METRIC SPACES

1Atilim University, Department of Mathematics, 06836, Incek, Ankara, TURKEY

2Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IRAN

3Department of Mathematics, Islamic Azad University, Science and Research Branch, 14778 93855 Tehran, IRAN

This content is open access.

Citation Information: Annals of the Alexandru Ioan Cuza University - Mathematics. Volume 0, Issue 0, Pages 65–78, ISSN (Print) 1221-8421, DOI: 10.2478/aicu-2013-0042, March 2014

Publication History

Published Online:
2014-03-25

Abstract

In this paper, we prove some common fixed point results for some mappings satisfying generalized contractive condition in complete partial metric space.

Keywords: fixed point; partial metric space

References

  • 1. Abdeljawad, T.; Karapinar, E.; Taş, K. - Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904. [CrossRef]

  • 2. Altun, I.; Simsek, H. - Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud., 1 (2008), 1-8.

  • 3. Altun, I.; Sola, F.; Simsek, H. - Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778-2785. [Web of Science]

  • 4. Aydi, H.; Karapinar, E.; Shatanawi, W. - Coupled fixed point results for (ψ, φ)- weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl., 62 (2011), 4449-4460. [CrossRef] [Web of Science]

  • 5. Banach, S. - Surles operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), 133-181.

  • 6. Beg, I.; Butt, A.R. - Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704.

  • 7. Border, K.C. - Fixed Point Theorems With Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985.

  • 8. Bukatin, M.; Kopperman, R.; Matthews, S.; Pajoohesh, H. - Partial metric spaces, Amer. Math. Monthly, 116 (2009), 708-718.

  • 9. ĆiriĆ, L.; Samet, B.; Aydi, H.; Vetro, C. - Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406. [Web of Science]

  • 10. Czerwik, S. - Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.

  • 11. Escardó, M.H. - PCF extended with real numbers. Real numbers and computers, Theoret. Comput. Sci., 162 (1996), 79-115.

  • 12. Fréchet, M. - Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22 (1906), 1-74. [CrossRef]

  • 13. Gillespie, J.B.; Houghton, C.J. - A metric space approach to the information channel capacity of spike trains, J. Comput. Neurosci., 30 (2011), 201-209. [CrossRef] [Web of Science]

  • 14. Heckmann, R. - Approximation of metric spaces by partial metric spaces, Applica- tions of ordered sets in computer science (Braunschweig, 1996), Appl. Categ. Struc- tures, 7 (1999), 71-83.

  • 15. Huang, L.-G.; Zhang, X. - Cone metric spaces and fixed point theorems of con- tractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.

  • 16. Karapinar, E. - Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., 2011, 2011:4, 7 pp.

  • 17. Karapinar, E.; Yüksel, U. - Some common fixed point theorems in partial metric spaces, J. Appl. Math., 2011, Art. ID 263621, 16 pp.

  • 18. Karapinar, E. - A note on common fixed point theorems in partial metric spaces, Miskolc Math. Notes, 12 (2011), 185-191.

  • 19. Karapinar, E.; Erhan, I.M. - Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899. [CrossRef] [Web of Science]

  • 20. Chi, K.P.; Karapinar, E.; Thanh, T.D. - A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55 (2012), 1673-1681. [Web of Science]

  • 21. Karapinar, E. - Weak ϕ-contraction on partial metric spaces, J. Comput. Anal. Appl., 14(2012), 206-210.

  • 22. Karapinar, E. - Some fixed point theorems on the class of comparable partial metric spaces, Appl. Gen. Topol., 12 (2011), 187-192.

  • 23. Karapinar, E.; Shobkolaei, N.; Sedghi, S.; Vaezpour, S.M. - A common fixed point theorem for cyclic operators on partial metric spaces, Filomat, 26 (2012), 407-414.

  • 24. Kopperman, R.D.; Matthews, S.G.; Pajoohesh, H. - What do partial metrics represent?, Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown, 2004.

  • 25. Kramosil, I.; Michálek, J. - Fuzzy metrics and statistical metric spaces, Kyber- netika (Prague), 11 (1975), 336-344.

  • 26. Künzi, H.-P.A.; Pajoohesh, H.; Schellekens, M.P. - Partial quasi-metrics, The- oret. Comput. Sci., 365 (2006), 237-246.

  • 27. Matthews, S.G. - Partial Metric Topology, Papers on general topology and appli- cations (Flushing, NY, 1992), 183-197, Ann. New York Acad. Sci., 728, New York Acad. Sci., New York, 1994.

  • 28. Matthews, S.G. - Partial Metric Topology, Research Report 212, Dept. of Com- puter Science, University of Warwick, 1992.

  • 29. Menger, K. - Statistical metrics, Proc. Nat. Acad. Sci. U.S.A., 28 (1942), 535-537. [CrossRef]

  • 30. Mustafa, Z.; Sims, B. - A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.

  • 31. Paesano, D.; Vetro, P. - Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920. [Web of Science]

  • 32. Romaguera, S. - A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., 2010, Art. ID 493298, 6 pp.

  • 33. Romaguera, S.; Schellekens, M. - Duality and quasi-normability for complexity spaces, Appl. Gen. Topol., 3 (2002), 91-112.

  • 34. Romaguera, S.; Schellekens, M. - Partial metric monoids and semivaluation spaces, Topology Appl., 153 (2005), 948-962.

  • 35. Romaguera, S.; Valero, O. - A quantitative computational model for complete partial metric spaces via formal balls, Math. Structures Comput. Sci., 19 (2009), 541-563. [Web of Science]

  • 36. Romaguera, S. - Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl., 159 (2012), 194-199. [Web of Science]

  • 37. Romaguera, S. - Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces, Appl. Gen. Topol., 12 (2011), 213-220.

  • 38. Schellekens, M.P. - A characterization of partial metrizability: domains are quan- tifiable, Topology in computer science (Schloß Dagstuhl, 2000), Theoret. Comput. Sci., 305 (2003), 409-432.

  • 39. Schellekens, M.P. - The correspondence between partial metrics and semivalua- tions, Theoret. Comput. Sci., 315 (2004), 135-149.

  • 40. Oltra, S.; Valero, O. - Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26 (2005).

  • 41. Shatanawi, W.; Samet, B.; Abbas, M. - Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling, 55 (2012), 680-687. [Web of Science]

  • 42. Shobkolaei, N.; Vaezpour, S.M.; Sedghi, S. - A common fixed point theorem on ordered partial metric spaces, J. Basic. Appl. Sci. Res., 1 (2011), 3433-3439.

  • 43. Stoy, J.E. - Denotational Semantics: the Scott-Strachey Approach to Programming Language Theory, Reprint of the 1977 original. With a foreword by Dana S. Scott. MIT Press Series in Computer Science, 1. MIT Press, Cambridge, Mass.-London, 1981.

  • 44. Waszkiewicz, P. - Partial metrisability of continuous posets, Math. Structures Com- put. Sci., 16 (2006), 359-372.

  • 45. Waszkiewicz, P. - Quantitative continuous domains, On formal description of computations-refined structures and new trends (Cork, 2000), Appl. Categ. Struc- tures, 11 (2003), 41-67.

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