Locally boundedness and continuity of superposition operators on double sequence spaces Cr0

Sağir B., Güngör N.

Journal of Computational Analysis and Applications, cilt.19, sa.2, ss.365-377, 2015 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2015
  • Dergi Adı: Journal of Computational Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.365-377
  • Anahtar Kelimeler: Continuity, Double sequence spaces, Locally bounded, Regularly convergent, Superposition operators
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

Let R be set of all real numbers, N be the set of all natural numbers and N2 = N×N. In this paper, we define the superposition operator Pg where g: N2×R → R by Pg ((xks)) = g(k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [11] have characterized Pg: c0 → l1 and Pg: c0 → lq where 1 ≤ q < ∞, respectively. The main aim of this paper is to construct the necessary and sufficient conditions for the boundedness and continuity of Pg: Cr0 → L1 and Pg: Cr0 → Lp where 1≤ p< ∞.