## Existence and uniqueness of a common fixed point on partial metric spaces.(English)Zbl 1230.54032

Summary: In this work, a general form of weak $$\phi$$-contraction is considered on partial metric spaces, to get a common fixed point. It is shown that self-mappings $$S,T$$ on a complete partial metric space $$X$$ have a common fixed point if they are generalized weak $$\phi$$-contractions.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects)
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### References:

 [1] S.G. Matthews, Partial metric topology, Research Report 212, Dept. of Computer Science, University of Warwick, 1992. · Zbl 0911.54025 [2] Matthews, S.G., Partial metric topology, (), 183-197 · Zbl 0911.54025 [3] Oltra, S.; Valero, O., Banach’s fixed point theorem for partial metric spaces, Rend. istit. mat. univ. trieste, 36, 1-2, 17-26, (2004) · Zbl 1080.54030 [4] Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. gen. topol., 6, 2, 229-240, (2005) · Zbl 1087.54020 [5] Altun, I.; Sola, F.; Simsek, H., Generalized contractions on partial metric spaces, Topology appl., 157, 18, 2778-2785, (2010) · Zbl 1207.54052 [6] Altun, I.; Erduran, A., Fixed point theorems for monotone mappings on partial metric spaces, Fixed point theory appl., 2011, (2011), Article ID 508730, 10 pages · Zbl 1207.54051 [7] Alber, Ya.I.; Guerre-Delabriere, S., Principle of weakly contractive maps in Hilbert space, (), 722 · Zbl 0897.47044 [8] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear anal., 47, 4, 2683-2693, (2001) · Zbl 1042.47521 [9] Boyd, D.W.; Wong, S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 458-464, (1969) · Zbl 0175.44903 [10] Hussain, N.; Jungck, G., Common fixed point and invariant approximation results for noncommuting generalized $$(f, g)$$-nonexpansive maps, J. math. anal. appl., 321, 851-861, (2006) · Zbl 1106.47048 [11] Song, Y., Coincidence points for noncommuting $$f$$-weakly contractive mappings, Int. J. comput. appl. math., 2, 1, 17-26, (2007) [12] Song, Y.; Xu, S., A note on common fixed-points for Banach operator pairs, Int. J. contemp. math. sci., 2, 1163-1166, (2007) · Zbl 1151.41311 [13] Zhang, Q.; Song, Y., Fixed point theory for generalized $$\varphi$$-weak contractions, Appl. math. lett., 22, 1, 75-88, (2009) · Zbl 1163.47304 [14] Păcurar, M.; Rus, I.A., Fixed point theory for cyclic $$\varphi$$-contractions, Nonlinear anal., 72, 3-4, 1181-1187, (2010) · Zbl 1191.54042 [15] E. Karapınar, Fixed point theory for cyclic weak $$\phi$$-contraction, Appl. Math. Lett., in press (doi:10.1016/j.aml.2010.12.016). · Zbl 1256.54073 [16] Abdeljawad, T.; Karapınar, E., Quasi-cone metric spaces and generalizations of Caristi kirk’s theorem, Fixed point theory appl., (2009), 9 pages · Zbl 1197.54051 [17] S. Moradi, Z. Fathi, E. Analouee, Common fixed point of single valued generalized $$\varphi_f$$-weak contractive mappings (in press). · Zbl 1296.54076
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