Cone Metric Spaces are usual Metric Spaces by a Renorming in the Banach Space

Abstract

In this paper, we will attempt to enforce the feeling that cone metric spaces are not real generalization of metric spaces, by a renorming of the Banach space. In specific, we can convert any strongly minihedral normal cone P to a normal cone with normal constant 1. Consequently, and due to this result, every cone metric space is really a metric space, and every theorem in metric spaces is valid for cone metric spaces automatically.