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In this paper, we prove that the Banach contraction principle proved by S. G.Matthews in 1994 on 0--complete partial metric spaces can be extended tocyclical mappings. However, the generalized contraction principle proved by D.Ili\'{c}, V. Pavlovi\'{c} and V. Rako\u{c}evi\'{c} in "Some new extensions ofBanach's contraction principle to partial metric spaces, Appl. Math. Lett. 24(2011), 1326--1330" on complete partial metric spaces can not be extended tocyclical mappings. Some examples are given to illustrate the effectiveness ofour results. Moreover, we generalize some of the results obtained by W. A.Kirk, P. S. Srinivasan and P. Veeramani in "Fixed points for mappingssatisfying cyclical contractive conditions, Fixed Point Theory 4 (1)(2003),79--89". Finally, an Edelstein's type theorem is also extended in caseone of the sets in the cyclic decomposition is 0-compact.

Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces