Main Article Content
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.
Article Details
References
- 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
- ap(n),
- (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
- ,73-74.
- 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.
References
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
ap(n),
(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
,73-74.
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.