## Generalized contractions on partial metric spaces.(English)Zbl 1207.54052

Topology Appl. 157, No. 18, 2778-2785 (2010); corrigendum ibid. 158, No. 13, 1738-1740 (2011).
In the present paper, the authors prove some fixed point theorems for generalized nonlinear contractive type mappings on complete partial metric spaces, including a Banach type fixed point theorem due to S. G. Matthews [Partial metric topology. Andima, Susan (ed.) et al., Papers on general topology and applications. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18–20, 1992. New York, NY: The New York Academy of Sciences. Ann. N. Y. Acad. Sci. 728, 183–197 (1994: Zbl 0911.54025)]. Moreover, a homotopy result on fixed points is given.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems

### Keywords:

fixed point; generalized contraction; partial metric space

Zbl 0911.54025
Full Text:

### References:

 [1] Agarwal, R.P.; O’Regan, D.; Sambandham, M., Random and deterministic fixed point theory for generalized contractive maps, Appl. anal., 83, 711-725, (2004) · Zbl 1088.47044 [2] Boyd, D.W.; Wong, J.S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 2, 458-465, (1969) · Zbl 0175.44903 [3] Ćirić, Lj.B., Fixed points for generalized multi-valued mappings, Mat. vesnik, 9, 24, 265-272, (1972) · Zbl 0258.54043 [4] Ćirić, Lj.B., Generalized contractions and fixed point theorems, Publ. inst. math., 12, 26, 19-26, (1971) · Zbl 0234.54029 [5] Escardo, M.H., PCF extended with real numbers, Theoret. comput. sci., 162, 79-115, (1996) · Zbl 0871.68034 [6] Hardy, G.E.; Rogers, T.D., A generalization of a fixed point theorem of Reich, Canad. math. bull., 16, 201-206, (1973) · Zbl 0266.54015 [7] Heckmann, R., Approximation of metric spaces by partial metric spaces, Appl. categ. structures, 7, 71-83, (1999) · Zbl 0993.54029 [8] Kannan, R., Some results on fixed points, Bull. Calcutta math. soc., 60, 71-76, (1968) · Zbl 0209.27104 [9] Kannan, R., Some results on fixed points-II, Amer. math. monthly, 76, 405-408, (1969) · Zbl 0179.28203 [10] Matkowski, J., Fixed point theorems for mappings with a contractive iterate at a point, Proc. amer. math. soc., 62, 2, 344-348, (1977) · Zbl 0349.54032 [11] Matthews, S.G., Partial metric topology, (), 183-197 · Zbl 0911.54025 [12] Oltra, S.; Valero, O., Banach’s fixed point theorem for partial metric spaces, Rend. istit. mat. univ. trieste, 36, 17-26, (2004) · Zbl 1080.54030 [13] O’Neill, S.J., Partial metrics, valuations and domain theory, (), 304-315 · Zbl 0889.54018 [14] Reich, S., Kannan’s fixed point theorem, Boll. unione mat. ital., 4, 4, 1-11, (1971) · Zbl 0219.54042 [15] Romaguera, S., A kirk type characterization of completeness for partial metric spaces, Fixed point theory appl., (2010), Article ID 493298, 6 pp · Zbl 1193.54047 [16] Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. gen. topol., 6, 2, 229-240, (2005) · Zbl 1087.54020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.