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

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. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 125–131, January, 2006.