Cone Normed Spaces
M. Eshaghi Gordji, M. Ramezani, H. Baghani, H. Khodaei
TL;DR
This paper introduces cone normed spaces and cone bounded linear mappings, establishing fundamental theorems like Baire category and Banach--Steinhaus within this new framework.
Contribution
It defines cone normed spaces and cone bounded linear mappings and proves key theorems, expanding the theory of normed spaces into cone structures.
Findings
Established the Baire category theorem in cone normed spaces.
Proved the Banach--Steinhaus theorem in cone normed spaces.
Introduced the concepts of cone normed spaces and cone bounded linear mappings.
Abstract
In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.
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Taxonomy
TopicsFixed Point Theorems Analysis · Advanced Banach Space Theory · Functional Equations Stability Results