Statistical cluster points of sequences in finite dimensional spaces
Version 2 2024-06-05, 03:23Version 2 2024-06-05, 03:23
Version 1 2019-07-18, 14:16Version 1 2019-07-18, 14:16
journal contribution
posted on 2024-06-05, 03:23authored byS Pehlivan, A Güngan, MA Mamedov
In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of T-statistical convergence. A sequence x is Γ-statistically convergent to a set C if C is a minimal closed set such that for every ε 0 the set {k: ρ(C,xk) ≥ ε} has density zero. It is shown that every statistically bounded sequence is Γ-statistically convergent. Moreover if a sequence is Γ-statistically convergent then the limit set is a set of statistical cluster points.