A Note on Statistical Limit and Cluster Points of The Arithmetical Functions ap(n), γ(n), and τ(n) in The Sense of Density

Abdu Awel Adem,Mehmet Kucukaslan

doi:10.22342/jims.26.2.808.224-233

Abdu Awel Adem, Mehmet Kucukaslan

Open Access

https://doi.org/10.22342/jims.26.2.808.224-233

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Abstract

In this paper, by using natural density of subsets of N, the statistical limit and cluster points of the arithmetical functions (ap (n)), γ (n),τ(n), Δ γ (n) and Δ τ (n) are studied. In addition to this, we also investigate statistical limit and cluster points of (Δ r γ (n) and (Δ r τ (n)) for each r ın N.

Highlights

In [3] and [12], Fast and Steinhaus introduced the concept of statistical convergence independently as a generalization of classical convergence
We will study the statistical limit and cluster points of the arithmetical function (ap(n))
It was especially focused on calculating the statistical limit and cluster points of some arithmetic functions

Summary

Introduction

In [3] and [12], Fast and Steinhaus introduced the concept of statistical convergence independently as a generalization of classical convergence. We are going to study the statistical limit and statistical cluster points of the arithmetic functions; ap(n), γ(n) and τ (n). A real number sequence x = (xk)∞ k=1 is statistically convergent to L provided that for every ε > 0 the set K(ε) = {k ∈ N : |xk − L| ≥ ε} has a natural density of zero.

Results

Conclusion