A Weak Contraction Principle in Partially Ordered Cone Metric Space with Three Control Functions

In this paper we utilize three functions to define a weak contraction in a cone metric space with a partial order and establish that this contraction has necessarily a fixed point either under the continuity assumption or an order condition which we state here. The uniqueness of the fixed point is also derived under some additional assumptions. The result is supported with an example. The methodology used is a combination of order theoretic and analytic approaches