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Fixed point theorems in convex partial metric spaces. (English) Zbl 1306.54057
Summary: Partial metric spaces were introduced by S. G. Matthews [in: 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)] as a part of the study of denotational semantics of dataflow networks, the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we study some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete partial metric space, these theorem generalize previously obtained results in convex metric space.

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