LOCALLY BOUNDEDNESS AND CONTINUITY OF SUPERPOSITION OPERATORS ON DOUBLE SEQUENCE SPACES C-r0
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, vol.19, no.2, pp.365-377, 2015 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 19 Issue: 2
- Publication Date: 2015
- Journal Name: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.365-377
- Keywords: Superposition Operators, Continuity, Locally Bounded, Double Sequence Spaces, Regularly Convergent
- Ondokuz Mayıs University Affiliated: Yes
Abstract
Let R be set of all real numbers, N be the set of all natural numbers and N-2 = N x N. In this paper, we define the superposition operator P-g where g : N-2 x R -> R by P-g ((x(ks))) = g (k, s, x(ks)) for all real double sequence (x(ks)). Chew & Lee [4] and Petranuarat & Kemprasit [11] have characterized P-g : c(0) -> l(1) and P-g : c(0) -> l(q) where 1 <= q < infinity, respectively. The main aim of this paper is to construct the necessary and sufficient conditions for the boundedness and continuity of P-g : C-r0 -> L-1 and P-g : C-r0 -> L-p where 1 <= p < infinity.