Strongly(V^λ, A, Δⁿ_(vm),p, q)-summable sequence spaces defined by modulus function and statistical convergence

Mohammad Aiyub

University of Bahrain

Kingdom of Bahrain 

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ABSTRACT

In this paper we introduce strongly (V^λ,A, Δⁿ_vm,p, q)-summable sequences and give the relation between the spaces of strongly (V^λ,A, Δⁿ_vm,p, q)-summable sequences and strongly (V^λ,A, Δⁿ_vm,p, q)-summable sequences with respect to a modulus function when A =(a_ik) is an infinite matrix of complex number, (Δⁿ_vm) is generalized difference operator, p = (p_i) is a sequence of positive real numbers and q is a seminorm. Also we give the relationship between strongly (V^λ,A, Δⁿ_vm,p, q) - convergence with respect to a modulus function and strongly S^λ(A, Δⁿ_(vm))- statistical convergence.

AMS Subject Classification (2000) : 40A05, 46A45.

Keywords and Phrases : De la Vallee-Poussin mean, Difference operator, modulus function, statistical convergence.

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M. Aiyub

Department of Mathematics, University of Bahrain,

P. O. Box-32038,

Kingdom of Bahrain

e-mail: maiyub2002@yahoo.com

Received : January 2015. Accepted : April 2015