Some Theorems and Examples of Cone Banach Spaces

ABDELJAWAD T., Turkoglu D., Abuloha M.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, cilt.12, sa.4, ss.739-753, 2010 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 4
  • Basım Tarihi: 2010
  • Dergi Adı: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.739-753
  • Anahtar Kelimeler: 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
  • Gazi Üniversitesi Adresli: Hayır

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.