Generalized Vector-Valued Sequence Spaces Defined by Modulus Functions

Abstract

We introduce the vector-valued sequence spaces w(infinity)(Delta(m),F,Q,p,u), w(1)(Delta(m),F,Q,p,u), and w(0)(Delta(m),F,Q,p,u), S-u(q) and S-0u(q), using a sequence of modulus functions and the multiplier sequence u = (u(k)) of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly Delta(m)u(q)-Cesaro summable with respect to the modulus function f then it is Delta(m)u(q)-statistically convergent.