Some Theorems and Examples of Cone Banach Spaces
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Date
2010
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Publisher
Eudoxus Press, Llc
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Abstract
In this paper, by defining a cone norm parallel to.parallel to(A) on E over itself which behaves like the absolute value norm on R, we construct examples of cone Banach spaces. Namely, we define the m-Euclidian cone normed space E-m, E-infinity and the space C-E(S) of continuous functions in cones, to generalize the Banach spaces R-m, l(infinity) and C [a, b], respectively. Some basic lemmas and theorems are also proved to help in the construction and in the proof of completeness of the above mentioned examples of cone normed spaces.
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Keywords
Cone Metric Space, Cone Normed Space, Cone Banach Space, Strongly Minihedral Cone, Limit Point In The Sense Of Cone, A-Property, Generalized Absolute Value Property, Space E-M, Space E-Infinity
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Citation
Abdeljawad, T., Türkoğlu, D., Abuloha, M. (2010). Some Theorems and Examples of Cone Banach Spaces. Journal of Computational analysis and Applications, 12(4), 739-753.
WoS Q
Scopus Q
Q4
Source
Volume
12
Issue
4
Start Page
739
End Page
753
