NEW FIXED-POINT THEOREMS ON PARTIALLY E-CONE METRIC SPACES

. In this paper, we extend the definition of partial metric space to a partially E-cone metric space partially ordered with a non-normal positive cone E+ of a real normed space E having empty interior. We prove an extension of some fixed point theorems of certain contractive maps in partially E-cone metric space to a larger class of cone metric spaces. Moreover, we establish some convergence properties of a sequence of elements in the sense partially E-cone metric space.