Some Theorems and Examples of Cone Banach Spaces


ABDELJAWAD T., Turkoglu D., Abuloha M.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, cilt.12, ss.739-753, 2010 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 12 Konu: 4
  • Basım Tarihi: 2010
  • Dergi Adı: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.739-753

Özet

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.