In this paper, we obtain a Quadruple fixed point theorem for ψ − φ contractive condition in partially ordered partial metric spaces by using ICS mapping. We are also given an example and an application to integral equation which supports our main theorem.2010 Mathematics Subject Classification. Primary: 47H10, 54H25.

Abstract. In this paper, we introduce the concept of (CLRS)-property for mappings F : XˆX Ñ X and S : X Ñ X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems. Introduction with preliminariesIn 2002, Aamri and El-Moutawakil [1] introduced the idea of the property (E.A) for a pair of self mappings defined on a metric space, which contains the classes of non-vacuously compatible as well as non-compatible mappings in metric spaces as proper subclasses and utilized the same to prove common fixed point theorems under strict contractive condition. Although the property (E.A) is a generalization of the concepts of non-compatible as well as non-vacuous compatible pairs, yet such results do require either completeness of the whole space or any one of the range subspaces or continuity conditions on the involved maps. But, quite contrary to this, the new notion of (CLR S )-property recently given by Sintunavarat and Kumam [8] does not impose such conditions. The importance of (CLR S )-property ensures that one does not require the completeness of the whole space or closedness of range subspaces.Nazir and Abbas [6] introduced the property (E.A) for a pair of self maps in partial metric spaces. In this paper, we introduce the concept of (CLR S )-property for the maps F : XˆX Ñ X and S : X Ñ X in a partial metric space and utilize the same to prove two unique common fixed point theorems for four mappings in partial metric spaces. As usual, let us denote 2010 Mathematics Subject Classification: 54H25, 47H10.

In this paper, we prove a tripled common fixed point theorem of Suzuki type for a pair of hybrid mappings in metric spaces. Our result generalizes and modifies several comparable results in the literature. We also provide an example to support our theorem.

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We prove the existence of a unique common coupled fixed point theorem for four mappings satisfying a general contractive condition on partial b-metric-like spaces. We also give an example to illustrate our main theorem. Our theorem generalizes and improves the theorem of [1].