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Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem

Yıl 2021, Cilt: 70 Sayı: 1, 279 - 289, 30.06.2021

Kamil Demirci Fadime Dirik Sevda Yıldız

https://doi.org/10.31801/cfsuasmas.807169
Cited By: 4

Öz

In this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.

Anahtar Kelimeler

Statistical convergence statistical relative uniform convergence Nörlund summability Korovkin-type approximation theorem modulus of continuity

Destekleyen Kurum

Sinop University

Proje Numarası

FEF-1901-18-25.

Teşekkür

This research was supported by Sinop University Scientific Research Coordination Unit, Project N. FEF-1901-18-25.

Kaynakça

  • Agnew, R.P., On deferred Cesàro means, Ann. Math., 33 (1932), 413-421. https://doi.org/10.2307/1968524
  • Altomare, F. and Campiti, M., Korovkin-Type Approximation Theory and Its Applications, de Gruyter Stud. Math. 17, Walter de Gruyter, Berlin, 1994. https://doi.org/10.1515/9783110884586
  • Anastassiou G. A. and Duman, O., Towards Intelligent Modeling: Statistical Approximation Theory, Intelligent Systems Reference Library, 14, Springer-Verlag, Berlin Heidelberg, 2011. https://doi.org/10.1007/978-3-642-19826-7
  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Triangular A-statistical approximation by double sequences of positive linear operators, Results. Math., 68 (2015), 271-291. https://doi.org/10.1007/s00025-015-0433-7
  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Korovkin-type theorems for modular Ψ- A- statistical convergence, J. Funct. Spaces, Article ID 160401 (2015), p. 11. https://doi.org/10.1155/2015/160401
  • Bardaro, C. and Mantellini, I., Korovkin's theorem in modular spaces, Commentationes Math., 47 (2007), 239-253. https://doi.org/10.14708/cm.v47i2.5253
  • Demirci, K. and Orhan, S., Statistically relatively uniform convergence of positive linear operators, Results. Math., 69 (2016), 359-367. https://doi.org/10.1007/s00025-015-0484-9
  • Dirik, F. and Demirci, K., Korovkin type approximation theorem for functions of two variables in statistical sense, Turk. J. Math., 34 (2010), 73-83. https://doi.org/10.3906/mat-0802-21
  • Dirik, F. and Demirci, K., Approximation in Statistical Sense to n-variate B-Continuous Functions by Positive Linear Operators, Math. Slovaca, 60 (2010), 877-886. https://doi.org/10.2478/s12175-010-0054-2
  • Duman, O. and Orhan, C., μ-statistically convergent function sequences, Czechoslovak Math. J., 54 (129) (2004), 413-422. https://doi.org/10.1023/B:CMAJ.0000042380.31622.39
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  • Gadjiev, A.D. and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32 (2002), 129-138. https://www.jstor.org/stable/44238888
  • Karakus, S., Demirci, K. and Duman, O., Equi-statistical convergence of positive linear operators, J. Math. Anal. Appl., 339 (2008), 1065-1072. https://doi.org/10.1016/j.jmaa.2007.07.050
  • Korovkin, P.P., Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
  • Niven, I. and Zuckerman, H.S., An Introduction to the Theory of Numbers, John Wiley and Sons, Fourt Ed., New York, 1980.
  • Söylemez, D. and Ünver, M., Korovkin type theorems for Cheney-Sharma operators via summability methods, Results. Math., 72(3) (2017) 1601-1612. https://doi.org/10.1007/s00025-017-0733-1
  • Steinhaus, H., Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math., 2 (1951), 73-74.
  • Srivastava, H. M. Bidu Bhusan Jena, Susanta Kumar Paikray, Misra, U. K., Generalized equi-statistical convergence of the deferred Nörlund summability and its applications to associated approximation theorems, RACSAM, 112 (2018), 1487-1501. https://doi.org/10.1007/s13398-017-0442-3
  • Tas, E. and Yurdakadim, T., Approximation by positive linear operators in modular spaces by power series method, Positivity, 21(4) (2017) 1293-1306. https://doi.org/10.1007/s11117-017-0467-z
  • Yılmaz, B., Demirci, K., Orhan, S., Relative Modular Convergence of Positive Linear Operators, Positivity, 20 (2016), 565-577. https://doi.org/10.1007/s11117-015-0372-2

Yıl 2021, Cilt: 70 Sayı: 1, 279 - 289, 30.06.2021

Kamil Demirci Fadime Dirik Sevda Yıldız

https://doi.org/10.31801/cfsuasmas.807169
Cited By: 4

Öz

Proje Numarası

FEF-1901-18-25.

Kaynakça

  • Agnew, R.P., On deferred Cesàro means, Ann. Math., 33 (1932), 413-421. https://doi.org/10.2307/1968524
  • Altomare, F. and Campiti, M., Korovkin-Type Approximation Theory and Its Applications, de Gruyter Stud. Math. 17, Walter de Gruyter, Berlin, 1994. https://doi.org/10.1515/9783110884586
  • Anastassiou G. A. and Duman, O., Towards Intelligent Modeling: Statistical Approximation Theory, Intelligent Systems Reference Library, 14, Springer-Verlag, Berlin Heidelberg, 2011. https://doi.org/10.1007/978-3-642-19826-7
  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Triangular A-statistical approximation by double sequences of positive linear operators, Results. Math., 68 (2015), 271-291. https://doi.org/10.1007/s00025-015-0433-7
  • Bardaro, C., Boccuto, A., Demirci, K., Mantellini, I., Orhan, S., Korovkin-type theorems for modular Ψ- A- statistical convergence, J. Funct. Spaces, Article ID 160401 (2015), p. 11. https://doi.org/10.1155/2015/160401
  • Bardaro, C. and Mantellini, I., Korovkin's theorem in modular spaces, Commentationes Math., 47 (2007), 239-253. https://doi.org/10.14708/cm.v47i2.5253
  • Demirci, K. and Orhan, S., Statistically relatively uniform convergence of positive linear operators, Results. Math., 69 (2016), 359-367. https://doi.org/10.1007/s00025-015-0484-9
  • Dirik, F. and Demirci, K., Korovkin type approximation theorem for functions of two variables in statistical sense, Turk. J. Math., 34 (2010), 73-83. https://doi.org/10.3906/mat-0802-21
  • Dirik, F. and Demirci, K., Approximation in Statistical Sense to n-variate B-Continuous Functions by Positive Linear Operators, Math. Slovaca, 60 (2010), 877-886. https://doi.org/10.2478/s12175-010-0054-2
  • Duman, O. and Orhan, C., μ-statistically convergent function sequences, Czechoslovak Math. J., 54 (129) (2004), 413-422. https://doi.org/10.1023/B:CMAJ.0000042380.31622.39
  • Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  • Gadjiev, A.D. and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32 (2002), 129-138. https://www.jstor.org/stable/44238888
  • Karakus, S., Demirci, K. and Duman, O., Equi-statistical convergence of positive linear operators, J. Math. Anal. Appl., 339 (2008), 1065-1072. https://doi.org/10.1016/j.jmaa.2007.07.050
  • Korovkin, P.P., Linear Operators and Approximation Theory, Hindustan Publ. Co., Delhi, 1960.
  • Niven, I. and Zuckerman, H.S., An Introduction to the Theory of Numbers, John Wiley and Sons, Fourt Ed., New York, 1980.
  • Söylemez, D. and Ünver, M., Korovkin type theorems for Cheney-Sharma operators via summability methods, Results. Math., 72(3) (2017) 1601-1612. https://doi.org/10.1007/s00025-017-0733-1
  • Steinhaus, H., Sur la convergence ordinaire et la convergence asymtotique, Colloq. Math., 2 (1951), 73-74.
  • Srivastava, H. M. Bidu Bhusan Jena, Susanta Kumar Paikray, Misra, U. K., Generalized equi-statistical convergence of the deferred Nörlund summability and its applications to associated approximation theorems, RACSAM, 112 (2018), 1487-1501. https://doi.org/10.1007/s13398-017-0442-3
  • Tas, E. and Yurdakadim, T., Approximation by positive linear operators in modular spaces by power series method, Positivity, 21(4) (2017) 1293-1306. https://doi.org/10.1007/s11117-017-0467-z
  • Yılmaz, B., Demirci, K., Orhan, S., Relative Modular Convergence of Positive Linear Operators, Positivity, 20 (2016), 565-577. https://doi.org/10.1007/s11117-015-0372-2
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Kamil Demirci 0000-0002-5976-9768

Fadime Dirik 0000-0002-9316-9037

Sevda Yıldız 0000-0002-4730-2271

Proje Numarası FEF-1901-18-25.
Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 7 Ekim 2020
Kabul Tarihi 22 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Demirci, K., Dirik, F., & Yıldız, S. (2021). Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 279-289. https://doi.org/10.31801/cfsuasmas.807169
AMA Demirci K, Dirik F, Yıldız S. Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):279-289. doi:10.31801/cfsuasmas.807169
Chicago Demirci, Kamil, Fadime Dirik, ve Sevda Yıldız. “Deferred Nörlund Statistical Relative Uniform Convergence and Korovkin-Type Approximation Theorem”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 279-89. https://doi.org/10.31801/cfsuasmas.807169.
EndNote Demirci K, Dirik F, Yıldız S (01 Haziran 2021) Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 279–289.
IEEE K. Demirci, F. Dirik, ve S. Yıldız, “Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 279–289, 2021, doi: 10.31801/cfsuasmas.807169.
ISNAD Demirci, Kamil vd. “Deferred Nörlund Statistical Relative Uniform Convergence and Korovkin-Type Approximation Theorem”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 279-289. https://doi.org/10.31801/cfsuasmas.807169.
JAMA Demirci K, Dirik F, Yıldız S. Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:279–289.
MLA Demirci, Kamil vd. “Deferred Nörlund Statistical Relative Uniform Convergence and Korovkin-Type Approximation Theorem”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 279-8, doi:10.31801/cfsuasmas.807169.
Vancouver Demirci K, Dirik F, Yıldız S. Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):279-8.

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