### ON CHARACTERIZATION OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN SOME SEQUENCE SPACES

#### Abstract

In this paper, we dene a non-Newtonian superposition operator

NPf where f : N R(N) ! R(N) by NPf (x) = (f (k; xk))1k=1 for every non-Newtonian real sequence (xk). Chew and Lee [4] have characterized Pf :`p ! `1 and Pf : c0 ! `1 for 1 p < 1 . The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NPf : `1 (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 : `1 (N) !

`1 (N) is *-continuous if and only if f(k; :) is *-continuous for every k 2 N.

NPf where f : N R(N) ! R(N) by NPf (x) = (f (k; xk))1k=1 for every non-Newtonian real sequence (xk). Chew and Lee [4] have characterized Pf :`p ! `1 and Pf : c0 ! `1 for 1 p < 1 . The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NPf : `1 (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 : `1 (N) !

`1 (N) is *-continuous if and only if f(k; :) is *-continuous for every k 2 N.

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