Mathematics

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A Comparative Study in Cone Metric Spaces and Cone Normed Spaces
(2016) Dua’a Abdullah Mohammad Al-Afghani; Dr. Abdallah A.Hakawati
Cone metric spaces are, not yet proven to be generalization of metric spaces. In many occasions the answer was proved, not to be affirmative. In this thesis we made a comparison between) Cone Metric Spaces and Cone Normed Spaces) and ( Ordinary Metric Spaces and Normed Spaces) as a way to find an answer for our main contribution. We choose the most important branches of mathematics to make a comparison as in: convergence, topology and best approximation theory. We also tried to transplant the idea of cone metric spaces in Orlicz’s spaces. We obtained new results while we investigate some properties which were proven to be incorrect in cone metric spaces but hold in ordinary case like as Sandwich Theorem, which gives us a sense of generality here.