The purpose of this manuscript is to present a fixed point theorem using a contractive condition of rational expression in the context of ordered partial metric spaces. | Fixed point theorem using a contractive condition of rational expression in the context of ordered partial metric spaces Nguyen Thanh Mai University of Science, Thainguyen University, Vietnam E-mail: thanhmai6759@ Abstract The purpose of this manuscript is to present a fixed point theorem using a contractive condition of rational expression in the context of ordered partial metric spaces. Mathematics Subject Classification: 47H10, 47H04, 54H25 Keywords: Partial metric spaces; Fixed point; Ordered set. 1 Introduction and preliminaries Partial metric is one of the generalizations of metric was introduced by Matthews[2] in 1992 to study denotational semantics of data flow networks. In fact, partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory [1, 4, 6, 7, 8, 11]. Recently, many researchers have obtained fixed, common fixed and coupled fixed point results on partial metric spaces and ordered partial metric spaces [3, 5, 6, 9, 10]. In [12] Harjani et al. proved the following fixed point theorem in partially ordered metric spaces. Theorem . ([12]). Let (X, ≤) be a ordered set and suppose that there exists a metric d in X such that (X, d) is a complete metric space. Let T : X → X be a non-decreasing mapping such that d(T x, T y) ≤ α d(x, T x)d(y, T y) + βd(x, y) for x, y ∈ X, x ≥ y, x 6= y, d(x, y) Also, assume either T is continuous or X has the property that (xn ) is a nondecreasing sequence in X such that xn → x, then x = sup{xn }. If there exists x0 ∈ X such that x0 ≤ T x0 , then T has a fixed point. In this paper we extend the result of Harjani, Lopez and Sadarangani [12] to the case of partial metric spaces. An example is considered to illustrate our obtained results. First, we recall some definitions of partial metric space and some of their properties [2, 3, 4, 5, 10]. Definition . A partial metric on a nonempty set X is a .
