On statistical convergence of vector-valued sequences associated with multiplier sequences - Altinok, H.; Et, M.; Gökhan, A. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We introduce vector-valued sequence spaces $w_{∞}(F, Q, p, u), w_{1}(F, Q, p, u), w_{0}(F, Q, p, u), S^q_u$ and $S^q_{0u}$, 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.