weak -contraction on partial metric spaces and existence of fixed points in partially ordered sets

[1] S.G. Matthews. Partial metric topology. Research Report 212. Dept. of Computer Science. University of Warwick, 1992.
[2] 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 Vol. 728 (1994), pp. 183-197.
[3] S. Oltra and O. Valero, Banach's fixed point theorem for partial metric spaces, Rendiconti dell'Istituto di Matematica dell'Universit di Trieste,
vol. 36, no. 1-2, pp. 17-26, 2004.
[4] O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology, vol. 6, no. 2, pp. 229-240, 2005.
[5] I. Altun, F. Sola, and H. Simsek, Generalized contractions on partial metric spaces, Topology and Its Applications, vol. 157, no. 18, pp. 2778¬2785, 2010.
[6] I. Altun and A. Erduran, Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces, Fixed Point Theory and Applications, vol. 2011, Article ID 508730, 10 pages, 2011. doi:10.1155/2011/508730
[7] Boyd D.W., Wong, .S.W.: On nonlinear contractions, Proc. Amer. Math. Soc. 20,458-464(1969).
[8] Alber,Ya. I., Guerre-Delabriere, S.: Principle of weakly contractive maps in Hilbert space In: I. Gohberg and Yu. Lyubich, Editors, New Results in Operator Theory, Advances and Appl. 98, Birkhâuser, Basel ,7-22,(1997).
[9] Rhoades, B. E.: Some theorems on weakly contractive maps. Nonlinear Anal., 47(4), 2683-2693, (2001).
[10] Hussain, N., Jungck, G.: Common fixed point and invariant approxima¬tion results for noncommuting generalized (f,g)-nonexpansive maps, J.
Math. Anal. Appl. 321, 851-861(2006).
[11] Song,Y.: Coincidence points for noncommuting f-weakly contractive mappings, Int. J. Comput. Appl. Math. (IJCAM) 2 (1),17-26 (2007).
[12] Song,Y. , S. Xu,S.: A note on common fixed-points for Banach operator
pairs, Int. J. Contemp. Math. Sci. 2, 1163-1166(2007).
[13] Zhang, Q.,Song,Y .: Fixed point theory for generalized t/?-weak contrac¬tions, Appl. Math. Lett. 22(1), 75-88(2009).
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Erdal Karapinar
[14] Pacurar, M., Rus, I.A.: Fixed point theory for cyclic ^-contractions, Non¬linear Anal., 72, (3-4),1181-1187 (2010).
[15] Abdeljawad, T. and Karapınar, E.: Quasi-Cone Metric Spaces and Gen¬eralizations of Caristi Kirk's Theorem. Fixed Point Theory Appl.,9 pages
doi:10.1155/2009/574387 (2009).
[16] E. Karapınar: Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl., (in press)