Generalized vector valued sequence spaces defined by Orlicz functions

Abstract

In this paper we introduce the vector valued sequence spaces w 0(M,?,? m, Q,p,u), w 1(M,?,? m, Q,p,u), w ?(M,?,? m, Q,p,u) and S?(? m uq) using an Orlicz function, the generalized difference operator ? m and the multiplier sequence u=(u k) of non-zero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly lacunary ? m uq- Cesàro summable with respect to the Orlicz function M then it is ? m uq- statistically convergent.