New Results on Cyclic Nonlinear Contractions in Partial Metric Spaces

Year 2015, Volume: 5 Issue: 2, 158 - 168, 01.12.2015

W.b. Domi S. Al-sharif H. Almefleh

Abstract

In this paper we study the concept of non-linear cyclic Kannan and Chatterjea contractions in partial metric spaces and we prove some new theorems on fixed point for these types of mappings extending some fixed point theorems in literature.

Keywords

cyclic contractions, partial metric, fixed point

References

• Mattews,S.G., (1992), Partial metric topology. research report 212. Department of Computer Science, University of warwick.
• Mattews,S.G., (1994), Partial metric topology. General Topology and its Applications. Proceedings of the 8th Summer Conference, Queen,s College. Ann NY Acad Sci, 728, pp. 183-197.
• Oltra,S. and Valero,O., Banach,s fixed point theorem for partial metric spaces. Rendiconti dell,Istituto di Mathematica dell,Universit di Trieste (2004), 36(1-2), pp. 17-26.
• Valero,O., On Banach,s fixed point theorems for partial metric spaces. Appl Gen Topol. 62 (2005), pp. 229-240.
• Altun,I., Sola,F. and Simsek,H., Generalized contractions on partial metric spaces. Topol Appl 157, 18 (2010), pp. 2778-2785.
• Altun,I. and Erduran,A., Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl (2011), pp. 10.
• Karapinar,E. and Inci,M., Fixed point theorems for operators on partial metric spaces. Appl Math Lett 24,11 (2011), pp. 1894-1899.
• Abdeljawad,T., Karapinar,E. and Tas,K., (2011), Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24, pp. 1900-1904.
• Nashine,H.K. and Kadelburg,Z., Cyclic contractions and fixed point results via control functions on partial metric spaces, International Journal of Analysis Volume 2013, Article ID 726387, pp. 9, http://dx.doi.org/10.1155/2013/726387.
• Banach,S., (1922), Surles operations dans les ensembles et leur application aux equation sitegrales, Fund. Math., 3, pp. 133-181.
• Nieto,J. and Rodriguez-Lopez,R., (2007), Existence and uniqueness of fixed point in partially orderded sets and applications to ordinary differential equations, Acta Math. Sinica, 23,12, pp. 2205-2210.
• Agarwal,R., El-Gebeily,M.A. and O’regan,D.,(2008), Generalized contraction in partially ordered met- ric spaces, Appl, Anal. 87, 1, pp. 109-116.
• Harjani,J. and Sadarangani,K., (2008), Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71 (7-8), pp. 3403-3410.
• Harjani,J. and Sadarangani,K., (2010), Generalized contractions in partialy ordered metric spaces and applications to ordinary equations, Nonlinear Anal. 72 (3-4), pp. 1188-1197.
• Kannan,R., (1968), Some results on fixed points, Bull. Calcutta Math. Soc. 10, pp. 71-76.
• Rus,I., (2005), Cyclic representations and fixed points, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 3, pp. 171-178.
• Chatterjea,S., (1972), Fixed point theorems, C. R. Acad. Bulgare Sci. 25, pp. 727-730.
• Petric,M., (2010), On some cyclical contractive conditions, General Mathematics 18, No. 4, pp. 213- 226.
• Choudhury,B.S., (2009), Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Tech. 5,1, pp. 6-13.
• Khan,M., Swaleh,M. and Sessa,S., (1984), Fixed point theorem by altering distances between points, bull. Austral. Math. Sos., 30(1), pp. 1-9.
• SastryK.R. and Babu,G.V., (1999), Some fixed point theorems by altering distances between the points, Indian Journal of Pure and Applied Mathematics, 30, 6, pp. 641-647.
• Sastry,K., Naidu,S., Babu,G. and Naidu,G.A., (2000), Generalization of common fixed point theorems for weakly commuting map by altering distances, Tamkang Journal of Mathematics, 31,3, pp. 243-250.
• Naidu,S., (2003), Some fixed point theorems in metric spaces by altering distances, Czechoslovak Mathematical Journal, 53,1, pp. 205–212.
• Sharifa Al-Sharif for the photography and short autobiography, see TWMS J. App. Eng. Math., V.4, N.2.