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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.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
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