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Zbl 1238.54017
Abdeljawad, Thabet; Karap inar, Erdal; Taş, Kenan
A generalized contraction principle with control functions on partial metric spaces. (English)
[J] Comput. Math. Appl. 63, No. 3, 716-719 (2012). ISSN 0898-1221

Summary: Partial metric spaces were introduced by {\it S. G. Matthews} [in: 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 data flow networks. We prove a generalized contraction principle with control functions $\varphi $ and $\psi $ on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions.

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: partial metric space; fixed point; generalized contraction principle; control functions

Citations: Zbl 0911.54025

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