Some Common Fixed Point Theorems Satisfying (ψ − φ) Maps in Partial Metric Spaces

Reza Arab^1,

¹Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

Cite this paper:
Reza Arab. Some Common Fixed Point Theorems Satisfying (ψ − φ) Maps in Partial Metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(2):53-60. doi: 10.12691/tjant-3-2-4

Abstract

In this paper, we present some coincidence and common fixed point results for infinite families of contractive maps satisfying a new class of pairs of generalized contractive type mappings defined in partial metric spaces. Our results extend and generalize many known results in the literature. Also, we introduce an example to support the validity of our results.

Keywords:
partial metric common fixed point coincidence point generalized contraction

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	T. Abdeljawad, E. Karapinar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Applied Mathematics Letters, 24(11)(2011),1900-1904.
[2]	I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl 2011, 10.
[3]	I. Altun, F. Sola, H. Simsek, Generalized contractions on Partial metric spaces, Topology and its Applications. 157 (2010) 2778-2785.
[4]	I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J Adv Math Stud. 1, (2008) 1-8.
[5]	I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl. 2011.
[6]	M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Am. Math. Mon. 116,(2009) 708-718.
[7]	E. Karapinar, M. E. Inci, Fixed point theorems for operators on partial metric spaces, Appl Math Lett 24 (11)(2011) 1894-1899.
[8]	S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197.
[9]	S. Oltra, O. Valero, Banachs fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste 36 (2004) 17-26.
[10]	S. J. ONeill, Two topologies are better than one, Tech. report, University of Warwick, Coven-try, UK, http://www.dcs.warwick.ac.uk/reports/283.html, 1995.
[11]	S. J. ONeill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 806, 1996, pp. 304-315.
[12]	S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. 2010 (Ar-ticle ID 493298),6 (2010).
[13]	S. Romaguera, O. Valero, A quantitative computational model for complete partial metric spaces via formal balls, Math. Structures Comput. Sci. 19 (3) (2009), 541-563.
[14]	B. Samet, M. Rajovic, R. Lazovi, R. Stoiljkovic, Common Fixed Point Results For Nonlinear Contractions in Ordered Partial Metric Spaces, Fixed Point Theory Appl. 2011.
[15]	O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol, 6 (2) (2005) 229-240.