Strongly (Vλ,A,P) ‐ summable sequence spaces defined by a modulus

Abstract

We introduce the strongly (V^λ,A,p) ‐ summable sequences and give the relation between the spaces of strongly (V^λ,A,p) ‐ summable sequences and strongly (V^λ,A,p) ‐ summable sequences with respect to a modulus function when A = (α _ik ) is an infinite matrix of complex numbers and ρ = (pi) is a sequence of positive real numbers. Also we give natural relationship between strongly (V^λ, A,p) ‐ convergence with respect to a modulus function and strongly S^λ (A) ‐ statistical convergence. Key words: De la Vallee‐Poussin mean, modulus function, statistical convergence.

First Published Online: 14 Oct 2010