Statistical convergence of order ɑ for difference sequences

Abstract

In this paper the concepts of Δ^m_v -statistical convergence of order ɑ and strong (p, Δ^m_v )-Cesàro summability of order ɑ are introduced for sequences of complex (or real) numbers. Some relations between the Δ^m_v -statistical convergence of order and strong (p, Δ^m_v )-Ces`aro summability of order ɑ are given. Also some relations between the space ω^ɑ_p (Δ^m_v, ƒ) and S^ɑ (Δ^m_v ) are examined.

Keywords: Sequences, statistical convergence, Cesàro summability.