Fixed point results for generalized cyclic contraction mappings in partial metric spaces

[EN] Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of a cyclic contraction mapping. Subsequently, Păcurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved several fixed point results for cyclic φ-contraction mappings in metric spaces. Karapınar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point for cyclic weak φ-contraction mappings and investigated the well-posedness problem for such mappings.

On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric in the context of studying the denotational semantics of dataflow networks, and proposed a modified version of the Banach contraction principle more suitable for this framework.

In this paper, we initiate the study of fixed points of generalized cyclic contractions within the framework of partial metric spaces. Several examples are also provided to illustrate and validate our results.