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Fixed point results for generalized cyclic contraction mappings in partial metric spaces. (English) Zbl 1256.54064
Summary: {\it I. A. Rus} [“Cyclic representations and fixed points”, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 3, 171--178 (2005)] introduced the concept of cyclic contraction mapping. {\it M. Păcurar} and {\it I. A. Rus} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No.  3--4, A, 1181--1187 (2010; Zbl 1191.54042)] proved some fixed-point results for cyclic $\phi$-contraction mappings on a metric space. {\it E. Karapınar} [Appl. Math. Lett. 24, No. 6, 822--825 (2011; Zbl 1256.54073)] obtained existence and uniqueness of fixed points of cyclic weak $\phi$-contraction mappings and studied the well-posedness problem for such mappings. On the other hand, {\it S. G. Matthews} [Ann. N. Y. Acad. Sci. 728, 183--197 (1994; Zbl 0911.54025)] introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.

54H25Fixed-point and coincidence theorems in topological spaces
54E35Metric spaces, metrizability
Full Text: DOI
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