CESARO AND STATISTICAL DERIVATIVE

Fatih Nuray

DOI Number
https://doi.org/10.22190/FUMI2005393N
First page
1393
Last page
1398

Abstract


In this study, we introduce the notions of Cesaro, strongly Ces`aro and statistical derivatives for real valued functions. These notions are based on the concepts of Cesaro and statistical convergence of a sequence. Then we establish some relationships between strongly Cesaro derivative and statistical derivative.


Keywords

Cesàro derivative; statistical derivative; Cesàro continuity; real valued functions; convergence of a sequence.

Full Text:

PDF

References


T. Acar and S. A. Mohiuddine: Statistical (C, 1)(E, 1) summability and Korovkin’s theorem. Filomat 30(2) (2016) 387–393.

C. Belen, and S. A. Mohiuddine: Generalized weighted statistical convergence and application. Appl. Math. Comput. 219 (2013) 9821–9826.

A. Borichev, R. Deville and E. Matheron: Strongly sequentially continuous

functions. Quaestiones Mathematicae, 24 (2001), 535–548.

J. S. Connor: The statistical and strong p-Ces´ aro of sequences. Analysis, 8(1988), 47–63.

J. Connor, and K.G. Grosse-Erdmann: Sequential definitions of continuity for real functions. Rocky Mountain J. Math., bf 33, 1, (2003), 93–121.

H. Fast: Sur la convergence statistique Cooloq. Math. 2(1951), 241–244.

J. A. Fridy: On statistical convergence Analysis, 5(1985), 301–313.

U. Kadak and S. A. Mohiuddine: Generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems. Results Math. 73(1) (2018), Article 9.

S. A. Mohiuddine: Statistical weighted A-summability with application to Korovkin’s type approximation theorem. J. Inequal. Appl. (2016) 2016:101.

S. A. Mohiuddine and B. A. S. Alamri: Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya

type approximation theorems. Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM 113(3) (2019) 1955–1973.

T. Sˇ alát: On statistically convergent sequences of real numbers. Math. Slovaca, 30(1980), 139–150.

S. Pedersen and J. P. Sjoberg: Sequential Derivatives, arXiv: 1801.04039v1 [math. CA] 12 Jan 2018.

H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math., 2(1951), 73–74.

I. J. Schoenberg: The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66 (1959), 361–375.




DOI: https://doi.org/10.22190/FUMI2005393N

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)