Generalized statistical convergence in 2-normed spaces

Abstract

In this paper we introduce the concept of λ-statistical convergence in 2-normed spaces. Some inclusion relations between the sets of statistically convergent, λ-statistically convergent and statistically λ-convergent sequences in 2-normed spaces are established, where λ = (λm) is a non-decreasing sequence of positive numbers tending to infinity such that λ_m+1 ≤ λ_m + 1, λ₁ = 1.