Fixed point theory for cyclic generalized contractions in partial metric spaces

for all x, y Î X, where : R+ ® R+ is a nondecreasing function such that lim n→∞ φ n(t) = 0 for all t > 0. In 1994, Matthews [4] introduced the notion of a partial metric space and obtained a generalization of Banach’s fixed point theorem for partial metric spaces. Recently, Altun et al. [5] (see also Altun and Sadarangani [6]) gave some generalized versions of the fixed point theorem of Matthews [4]. Di Bari and Vetro [7] obtained some results concerning cyclic mappings in the framework of partial metric spaces. We recall below the definition of partial metric space and some of its properties (see [4,5,8,9]). Definition 1 A partial metric on a nonempty set X is a function p : X × X ® R+ such that for all x, y, z, Î X: Agarwal et al. Fixed Point Theory and Applications 2012, 2012:40 http://www.fixedpointtheoryandapplications.com/content/2012/1/40