MEMETRIKKAN RUANG MERIK CONE DENGAN MENORMKAN RUANG BANACH

Abstract

Huang and Zhang introduced the cone metric space, by replacing codomain from the set of real numbers into an ordered Banach space on a cone, where the cone is a non empty subset of real Banach space that satisfy certain other properties. In this study also explained about the norm space which is a pair of a vector space with a norm that satisfy some specific properties. Furthermore, Banach space is a complete norm space and space norm says completed if every Chaucy sequence in norm space is convergent.
In this paper, the researcher want to study how to metrizability of metric spaces via renorming the Banach spaces. This research was conducted by explaining and proving how to metrizability of cone metric spaces via renorming the Banach spaces. The result is a metric space cone can be made into an ordinary metric space with a metric defined by 𝑑𝑑(𝜑𝜑,𝜓𝜓)=‖|𝐷𝐷(𝜑𝜑,𝜓𝜓)|‖