On statistical convergence of vector-valued sequences associated with multiplier sequences

Abstract

We introduce vector-valued sequence spaces w ?(F, Q, p, u), w 1(F, Q, p, u), w 0(F, Q, p, u), S u q , and S 0u q using a sequence of modulus functions and a multiplier sequence u = (u k ) of nonzero complex numbers. We give some relations for these sequence spaces. It is also shown that if a sequence is strongly u q -Cesàro summable with respect to the modulus function, then it is u q -statistically convergent. © 2006 Springer Science+Business Media, Inc.