2017
Том 69
№ 6

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

Abstract

We introduce vector-valued sequence spaces $w_{\infty}(F, Q, p, u), w_{1}(F, Q, p, u), w_{0}(F, Q, p, u), S^q_u$ 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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 1, pp 139-146.

Citation Example: Altinok H., Et M., Gökhan A. On statistical convergence of vector-valued sequences associated with multiplier sequences // Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 125–131.

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