New Fixed-Point Theorems on Partially E-Cone Metric Spaces

Abstract

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.

Key words and phrases. Partial E-cone metric space, Semi-interior points, Fixed point.

2020 Mathematics Subject Classification. 15A18, 15A60, 47A30, 47B15