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Fixed point theorems for generalized contractions on partial metric spaces. (English) Zbl 1232.54039
Author’s abstract: We obtain two fixed point theorems for complete partial metric spaces that, on one hand, clarify and improve some results that have been recently published in Topology and its Applications, and on the other hand, generalize in several directions the celebrated Boyd and Wang fixed point theorem and Matkowski fixed point theorem, respectively.

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Altun, I.; Sadarangani, K.: Corrigendum to ”generalized contractions on partial metric spaces” [Topology appl. 157 (2010) 2778-2785], Topology appl. 158, 1738-1740 (2011) · Zbl 1226.54041
[2] Altun, I.; Sola, F.; Simsek, H.: Generalized contractions on partial metric spaces, Topology appl. 157, 2778-2785 (2010) · Zbl 1207.54052 · doi:10.1016/j.topol.2010.08.017
[3] Boyd, D. W.; Wong, J. S. W.: On nonlinear contractions, Proc. amer. Math. soc. 20, 458-464 (1969) · Zbl 0175.44903 · doi:10.2307/2035677
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[6] Matkowski, J.: Integrable solutions of functional equations, Dissertationes math. 127, 1-68 (1975) · Zbl 0318.39005
[7] Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point, Proc. amer. Math. soc. 62, 344-348 (1977) · Zbl 0349.54032 · doi:10.2307/2041041
[8] Romaguera, S.; Schellekens, M.: Partial metric monoids and semivaluation spaces, Topology appl. 153, 948-962 (2005) · Zbl 1084.22002 · doi:10.1016/j.topol.2005.01.023
[9] Romaguera, S.; Valero, O.: A quantitative computational model for complete partial metric spaces via formal balls, Math. structures comput. Sci. 19, 541-563 (2009) · Zbl 1172.06003 · doi:10.1017/S0960129509007671
[10] Schellekens, M. P.: A characterization of partial metrizability. Domains are quantifiable, Theoret. comput. Sci. 305, 409-432 (2003) · Zbl 1043.54011 · doi:10.1016/S0304-3975(02)00705-3
[11] Waszkiewicz, P.: Quantitative continuous domains, Appl. categ. Structures 11, 41-67 (2003) · Zbl 1030.06005 · doi:10.1023/A:1023012924892