Coupled Fixed Point Theorems for Symmetric \((\phi,\psi )\)-weakly Contractive Mappings in Ordered Partial Metric Spaces

Volume 7, Issue 4, pp 276 - 292 http://dx.doi.org/10.22436/jmcs.07.04.07

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Authors

Manish Jain - Department of Mathematics, Ahir College, Rewari 123401, India. Neetu Gupta - HAS Department, YMCAUST, Faridbad, India. Calogero Vetro - Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy. Sanjay Kumar - Department of Mathematics, DCRUST, Murthal, Sonepat, India.

Abstract

We establish some coupled fixed point theorems for symmetric \((\phi,\psi)\)-weakly contractive mappings in ordered partial metric spaces. Some recent results of Berinde (Nonlinear Anal. 74 (2011), 7347-7355; Nonlinear Anal. 75 (2012), 3218-3228) and many others are extended and generalized to the class of ordered partial metric spaces.

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Keywords

• Coupled fixed point
• Partial metric space
• Contractions
• Mixed monotone property.

MSC

•  47H10
•  54E40
•  54F05

References

• [1] V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings partially ordered metric spaces, Nonlinear Anal. , 74 (2011), 7347–7355.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] V. Berinde, Coupled fixed point theorems for \(\phi\)-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. , 75 (2012), 3218–3228.
  • View Article
  • MathSciNet
  • Google Scholar


• [3] S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and applications, in: Ann. New York Acad. Sci., 728 (1994), 183–197.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. , 6 (2005), 229–240.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] S. Oltra, O. Valero , Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste , 36 (2004), 17–26.
  • MathSciNet
  • Google Scholar


• [6] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. , 157 (2010), 2778–2785.
  • Google Scholar


• [7] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , 132 (2004), 1435–1443.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] J. J. Nieto, R. R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) , 23 (12) (2007), 2205–2212.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal. , 87 (2008), 1–8.
  • View Article
  • Google Scholar


• [10] I. Altun, H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. Article ID 621469 , 2010 (2010), 17 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [11] J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. , 72 (2010), 1188–1197.
  • View Article
  • MathSciNet
  • Google Scholar


• [12] Z. Kadelburg, M. Pavlović, S. Radenović, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl., 59 (2010), 3148–3159.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] S. Radenović, Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. , 60 (2010), 1776–1783.
  • View Article
  • Google Scholar


• [14] W. Sintunavarat, Y. J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. , 62 (2011), 1969–1978.
  • View Article
  • MathSciNet
  • Google Scholar


• [15] T. G. Bhaskar, V. Lakshmikantham , Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
  • View Article
  • Google Scholar


• [16] N. V. Luong, N. X. Thuan, Coupled fixed point in partially ordered metric spaces and applications, Nonlinear Anal. , 74 (2011), 983–992.
  • View Article
  • Google Scholar


• [17] I. Altun, A. Erdran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., Article ID 508730, 2010 (2010), 10 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [18] I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. , 1 (2008), 1–8.
  • MathSciNet
  • Google Scholar


• [19] H. Aydi, Some coupled fixed point results on partial metric spaces, Int. J. Math. Math. Sci. Article ID 647091, , 2011 (2011), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [20] R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures , 7 (1999), 71–83.
  • View Article
  • MathSciNet
  • Google Scholar


• [21] Th. Abdeljawad, E. Karapinar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. , 24 (2011), 1900–1904.
  • View Article
  • MathSciNet
  • Google Scholar


• [22] Th. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Comput. Math. Appl., 2923-2927 (2011)
  • View Article
  • MathSciNet
  • Google Scholar


• [23] E. Karapinar, I. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894–1899.
  • View Article
  • MathSciNet
  • Google Scholar


• [24] D. Ilić, V. Pavlović, V. Rakoćevic , Some new extensions of Banach’s contraction principle to partial metric space , Appl. Math. Lett. , 24 (8) (2011), 1326–1330.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] E. Karapinar, Weak \(\phi\)-contarction on partil contraction and existence of fixed points in partilally orederd sets, Math. Aeterna , 1 (4) (2011), 237–244.


• [26] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces , Fixed Point Theory Appl., Article ID 493298, 2010 (2010), 6 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] A. I. Rus , Fixed point theory in partial metric spaces, An. Univ. Vest Timis., Ser. Mat.-Inform. XLVI, 2 (2008), 149–160.


• [28] B. Samet, M. Rajovi𝑐𝑐́, R. Lazovi𝑐𝑐́, R. Stojiljkovi𝑐𝑐́, Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. , (2011)
  • MathSciNet
  • Google Scholar


• [29] W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling , 55 (2012), 680–687.
  • View Article
  • MathSciNet
  • Google Scholar


• [30] S. Alsulami, N. Hussain, A. Alotaibi , Coupled fixed and coincidence points for monotone operators in partial metric spaces, Fixed Point Theory Appl. , 2012 (2012), 173
  • View Article
  • MathSciNet
  • Google Scholar


• [31] H. Aydi , Coupled fixed point results in ordered partial metric spaces, Selcuk J. Appl. Math. , 13 (1) (2012), 23–33.
  • Google Scholar


• [32] B. Samet, H. Yazidi, Coupled fixed point theorems in partially ordered \(\varepsilon\)-chainable Metric spaces , The Journal of Mathematics and Computer Science , 1(3) (2010), 142–151.
  • Google Scholar


• [33] S. H. Rasouli, M. Bahrampour, A remark on the coupled fixed point theorems for mixed monotone operators in partially ordered metric spaces, The Journal of Mathematics and Computer Science , 3(2) (2011), 246–261.
  • Google Scholar