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


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.

Full Text:



Connor, J. S., (1988) The statistical and strong p-Cesaro convergence of sequences, Analysis,

VOL, 8, 47{63.

Fast, H. , (1951) Sur la convergence statistique., Colloq.Math, VOL, 2, 241{244.

Fehera, Z., Laszloa, B., Macajb, M., & Salatb, T., (2006) Remarks on arithmetical functions


(n), (n), Annales Mathematicae et Informaticae, VOL, 33, 35{43.

Fridy, J. A., (1985) On statistical convergence, Analysis, VOL, 5, 301{313.

Fridy J. A., Miller H. I., (1991) A matrix characterization of statistical convergence, Analysis,

VOL, 11, 59{66.

Fridy, J. A., (1993) Statistical limit points, Proceedings of the American Mathematical Soci-

ety, VOL, 118,Num, 4, 1187{1192.

Milan, P. (2017) DENSITY AND RELATED TOPICS, Page 8-10,

Mycielski, J. (1951) Sur les representations des nombres naturels par des puissances a base

et exposant naturels, Colloquium Mathematicum, VOL, 2, 254{260.

Schoenberg, I. J., (1959) The integrability of certain functions and related summability meth-

ods, matrix characterization of statistical convergence, Amer.Math., VOL, 66, 361{375.

Steinhaus H. , Sur la convergence ordinaire at la convergence asymptotique, Colloc.Math. 2.1


Salat, T., (1994) On the function ap; pap(n)nn n (n > 1) , Mathematica Slovaca, VOL, 44,

Num, 2 143{151.

Zygmund, A. (1979) Trigonometric series, 2nd., Ed. Vol. II, Cambridge Univ. press, London

and New York.

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


  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats