Let $\lambda $ and $\mu $ be solid sequence spaces. For a sequence of modulus functions $\Phi =(\varphi _{k})$ let $ \lambda (\Phi )= \lbrace x=(x_{k}) \: (\varphi _{k}(|x_{k}|))\in \lambda \rbrace $. Given another sequence of modulus functions $\Psi =(\psi _{k})$, we characterize the continuity of the superposition operators ${P_{f}}$ from $\lambda (\Phi )$ into $\mu (\Psi )$ for some Banach sequence spaces $\lambda $ and $\mu $ under the assumptions that the moduli $\varphi _{k}$ $(k \in \mathbb{N})$ are unbounded and the topologies on the sequence spaces $\lambda (\Phi )$ and $\mu (\Psi )$ are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type.
The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in $2$-normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.