A generalization of Banachs contraction principle for nonlinear contraction in a partial metric space

Volume 5, Issue 1, pp 37--43 http://dx.doi.org/10.22436/jnsa.005.01.05

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1638 Downloads
• 2440 Views

Authors

Wasfi Shatanawi - Department of Mathematics, Hashemite University, Zarqa, Jordan. Hemant Kumar Nashine - Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Naradha, Mandir Hasaud, Raipur-492101 (Chhattisgarh), India.

Abstract

We establish a fixed point theorem for nonlinear contraction in a complete partial metric space. Our result generalizes the Banach type fixed point theorem in a partial metric space in the sense of Matthews.

Share and Cite

Keywords

• Partial metric space
• Banach principle
• Fixed Point Theory.

MSC

•  54H25
•  47H10

References

• [1] I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory, Article ID 508730, 2011 (2011), 10 pages.


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


• [3] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157(18) (2010), 2778-2785.


• [4] H. Aydi, Some fixed point results in ordered partial metric spaces, accepted in J. Nonlinear Sci. Appl., (2011)


• [5] H. Aydi, E. Karapinar, W. Shatanawi, Coupled fixed point results for (\(\psi,\phi\))-weakly contractive condition in ordered partial metric spaces, Computer Math. Appl, 62 (2011), 4446-4460.


• [6] V. Berinde, Some remarks on a fixed point theorem for Ciric-type almost contractions, Carpathian J. Math. , 25 (2009), 157-62.


• [7] V. Berinde, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math. , 24 (2008), 9-10.


• [8] Lj B. Ćirić, Generalized contractions and fixed-point theorems, Publ. lInst Math. (Beograd) , 12 (1971), 19-26.


• [9] Lj B. Ćirić, A generalization of Banachs contraction principle , Proc Amer. Math. Soc. , 45 (1974), 267-73.


• [10] Lj B. Ćirić, On contraction type mappings, Math Balkanica , 1 (1971), 527


• [11] Lj B. Ćirić, Fixed point theory, Contraction Mapping principle, FME Press, Beograd (2003)


• [12] Lj B. Ćirić, Coincidence and fixed points for maps on topological spaces, Topol. Appl. , 154 (2007), 3100-3106.


• [13] Lj B. Ćirić, Fixed point theorems for multi-valued contractions in complete metric spaces, J. Math. Anal. Appl. , 348 (2008), 499-507.


• [14] Lj B. Ćirić, Non-self mappings satisfying nonlinear contractive condition with applications, Nonlinear Anal., 71 (2009), 2927-2935.


• [15] Lj B. Ćirić, M. Abbas, R. Saadati, N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput. , 227 (12) (2011), 5784-5789.


• [16] Lj B. Ćirić, N. Cakić, M. Rajovi, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. Article ID 131294, 2008 (2008), 11 pages.


• [17] Lj B. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. , 218 (2011), 2398-2406.


• [18] R. Heckmann , Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures , 7 (1999), 71-83.


• [19] D. Ilić, V. Pavlović, V. Rakočević, Some new extensions of Banach's contraction princible to partial metric space, Appl. Math. Lett. , doi:10.1016/j.aml.2011.02.025 (2011)


• [20] E. Karapınar, Weak \(\phi\)-contraction on partial contraction, J. Comput. Anal. Appl. , (in press)


• [21] E. Karapınar, Generalizations of Caristi Kirk's Theorem on Partial metric Spaces, Fixed Point Theory Appl., (in press),


• [22] S. G. Matthews, Partial metric topology, In, General Topology and its Applications, Proc. 8th Summer Conf., Queen's College (1992), Annals of the New York Academy of Sciences, 728 (1994), 183-197.


• [23] H. K. Nashine, Fixed point results for mappings satisfying ( \(\psi,\varphi\))-weakly contractive condition in ordered partial metric spaces, accepted in Math. , Slovaca (2011)


• [24] O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology , 6(2) (2005), 229- 240.


• [25] S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rendiconti dell'Istituto di Matematica dell'Universit di Trieste, 36(1-2) (2004), 17-26.


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


• [27] B. Samet, C. Vetro , An integral version of Ćirić s fixed point theorem, Mediterr J Math. , doi:10.1007/s00009- 011-0120-1. ()


• [28] W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Mod., doi:10.1016/j.mcm.2011.08.042. (2011)