On characterization of non-Newtonian superposition operators in some sequence spaces

Abstract

In this paper, we define a non-Newtonian superposition operator NPf where f : N x R(N)? ? R(N)? by NPf (x) = (f(k,xk))? k=1 for every non-Newtonian real sequence x = (xk). Chew and Lee [4] have characterized Pf : ?p ? ?1 and Pf : c0 ? ?1 for 1 ? p < ?. The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NPf : ?? (N) ??1(N), NPf: c0(N)??1(N), NPf : c (N)? ?1 (N) and NPf : ?p (N) ? ?1 (N), respectively. Then we show that such NPf : ??(N) ? ?1 (N) is *-continuous if and only if f (k,.) is *-continuous for every k ? N.