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- MakaleYalnız künye2017Continuity of superposition operators on the double sequence spaces of maddox L(p)
Güngör, Nihan; Sağır, Birsen
Petranuarat and Kemprasit (Southeast Asian Bull Math 21:139–147, 1997) characterized continuity of the superposition operator acting from the sequence space lp into lq where 1 ≤ p, q < ∞. Sağır and Güngör defined the superposition operator Pg by Pg(x) = (g(k, s, xks))∞k,s=1 for all real double sequences (xks) where g: N2 × R → R and gave continuity of the superposition operator acting from the double sequence spaces Lp into Lq for 1 ≤ p, q < ∞. In this paper, we characterize the continuity of the superposition operator acting from Maddox double sequence spaces L(p) into L(q)where p = (pks) and q = (qks) are bounded double sequences of positive numbers.
- MakaleYalnız künye2015Locally boundedness and continuity of superposition operators on double sequence spaces Cr0
Sağir, Birsen; Güngör, Nihan
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< ∞.
- MakaleAçık Erişim2015Continuity of superposition operators on the double sequence spaces Lp
Sağır, Birsen; Güngör, Nihan
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 [7] have characterized Pg : lp → l1 and Pg : lp → lq where 1 ≤ p; q < ∞, respectively. The main goal of this paper is to construct the necessary and sucient conditions for the continuity of Pg : Lp → L1 and Pg : Lp → Lq where 1 _ p; q < ∞.