(λ, μ)-Statistical convergence of double sequences in n-normed spaces

Hazarika B., Savaş E.

Note di Matematica, vol.32, no.2, pp.101-114, 2012 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1285/i15900932v32n2p101
  • Journal Name: Note di Matematica
  • Journal Indexes: Scopus
  • Page Numbers: pp.101-114
  • Keywords: λ-Statistical convergence, double sequence, N-norm, Statistical convergence
  • Uşak University Affiliated: No

Abstract

In this paper, we introduce the concept of (λ, μ)-statistical convergence in n-normed spaces, where λ = (λr) and μ = (μs) be two non-decreasing sequences of positive real numbers, each tending to ∞ and such that λr+1 ≤ λr + 1, λ1 = 1; μs+1 ≤ μs + 1, μ1 = 1. Some inclusion relations between the sets of statistically convergent and (λ, μ)-statistically convergent double sequences are established. We find its relation to statistical convergence, (C, 1, 1)-summability and strong (V, λ, μ)-summability in n-normed spaces. © 2012 Università del Salento.