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

54H25Fixed-point and coincidence theorems in topological spaces
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
[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 · doi:10.1080/00036810410001657206
[2]Boyd, D. W.; Wong, J. S. W.: On nonlinear contractions, Proc. amer. Math. soc. 20, No. 2, 458-465 (1969)
[3]Ćirić, Lj.B.: Fixed points for generalized multi-valued mappings, Mat. vesnik 9, No. 24, 265-272 (1972) · Zbl 0258.54043
[4]Ćirić, Lj.B.: Generalized contractions and fixed point theorems, Publ. inst. Math. 12, No. 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 · doi:10.1016/0304-3975(95)00250-2
[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 · doi:10.4153/CMB-1973-036-0
[7]Heckmann, R.: Approximation of metric spaces by partial metric spaces, Appl. categ. Structures 7, 71-83 (1999) · Zbl 0993.54029 · doi:10.1023/A:1008684018933
[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 · doi:10.2307/2316437
[10]Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point, Proc. amer. Math. soc. 62, No. 2, 344-348 (1977) · Zbl 0349.54032 · doi:10.2307/2041041
[11]Matthews, S. G.: Partial metric topology, Ann. New York acad. Sci. 728, 183-197 (1994) · 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, Ann. New York acad. Sci. 806, 304-315 (1996) · Zbl 0889.54018
[14]Reich, S.: Kannan’s fixed point theorem, Boll. unione mat. Ital. 4, No. 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) · Zbl 1193.54047 · doi:10.1155/2010/493298
[16]Valero, O.: On Banach fixed point theorems for partial metric spaces, Appl. gen. Topol. 6, No. 2, 229-240 (2005) · Zbl 1087.54020