Thabet Abdeljawad, Jehad O. Alzabut, Aiman Mukheimer, Younes Zaidan
Published 2011-12-26Version 1
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 to cyclical 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 of Banach's contraction principle to partial metric spaces, Appl. Math. Lett. 24 (2011), 1326--1330" on complete partial metric spaces can not be extended to cyclical mappings. Some examples are given to illustrate the effectiveness of our results. Moreover, we generalize some of the results obtained by W. A. Kirk, P. S. Srinivasan and P. Veeramani in "Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003),79--89". Finally, an Edelstein's type theorem is also extended in case one of the sets in the cyclic decomposition is 0-compact.
Best proximity point results in topological spaces and extension of Banach contraction principle
On Frink's metrization technique and applications
Some extensions of Banach'\ CP in $G$-metric spaces
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