BibTex RIS Kaynak Göster

Quantitative estimates for Jain-Kantorovich operators

Yıl 2016, Cilt: 65 Sayı: 2, 121 - 132, 01.08.2016
https://doi.org/10.1501/Commua1_0000000764

Öz

By using given arbitrary sequences,property that limn 1nn= 0and limn 1 n= 0, we give a Kantorovichtype generalization of Jain operator based on the a Poisson disrtibition. Fristlywe give the quantitative Voronovskaya type theorem. Then we also obtain theGrüss Voronovskaya type theorem in quantitative form .We show that theyhave an arbitrary good order of weighted approximation

Kaynakça

  • T. Acar, A. Aral and I. Ra¸sa, The new forms of Voronovskaya’s theorem in weighted spaces, Positivity, 20 (1) (2016), 25-40.
  • A. Aral, E. Deniz and V. Gupta, On Modi…cation of the Szasz-Durrmeyer Operators, Sub- mitted. O. Agratini, On an approximation process of integral type, App. Math. and Comput., 236 (2014), 195–201.
  • O. Agratini, Kantorovich sequences associated to general approximation processes, Positivity, (4) (2015), 681-693.
  • P.L. Butzer, On the extensions of Bernstein polynomials to the in…nite interval, Proc. Amer. Math. Soc., 5 (1954), 547–553.
  • O. Do¼gru, On a certain family of linear positive operators. Turkish J. Math., 21 (4) (1997), 399.
  • A. D. Gadjiev, R. O. Efendiyev and E. Ibikli, On Korovkin type theorem in the space of locally integrable functions, Czech. Math. J., 53 (128) (2003), 45-53.
  • A. D. Gadzhiev, Theorems of the of P. P. Korovkin type theorems, Math. Zametki, 20 (5) (1976), 781-786; Math. Notes, 20 (5-6) (1976), 996-998 (English Translation).
  • S. G. Gal and H. Gonska, Grüss and Grüss-Voronovskaya-type estimates for some Bernstein- type polynomials of real and complex variables, arXiv: 1401.6824v1.
  • V. Gupta and G. C. Greubel, Moment Estimations of New Szász-Mirakyan-Durrmeyer Op- erators, Appl. Math. Comput. 271 (2015), 540–547.
  • V. Gupta and R. P. Pant, Rate of convergence for the modi…ed Szász Mirakyan operators on functions of bounded variation, J. Math. Anal. Appl., 233 (2) (1999), 476-483.
  • N. Ispir, On modi…ed Baskakov operators on weighted spaces, Turk. J. Math., 26 (3) (2001) 365.
  • A. Olgun, F. Ta¸sdelen and A. Erençin, A generalization of Jain’s operators, App. Math. and Comput., 266 (2015), 6–11.
  • G. C. Jain, Approximation of functions by a new class of linear operators, J. Austral. Math. Soc., 13 (3) (1972), 271-276.
  • O. Szasz, Generalization of S. Bernstein’s polynomials to the in…nite interval, J. of Research of the Nat. Bur. of Standards, 45 (1950), 239-245.
  • S. Tarabie, On Jain-Beta Linear Operators, Appl. Math. Inf. Sci., 6 (2) (2012), 213-216.
  • S. Umar and Q. Razi, Approximation of function by a generalized Szász operators, Commu- nications de la Fac. Sci. L’Univ D’Ankara, 34 (1985), 45-52.
  • Current address : Department of Mathematics, Faculty of Science and Arts, Kirikkale Univer- sity, 71450 Yahsihan, Kirikkale, Turkey
  • E-mail address : emredeniz--@hotmail.com
Yıl 2016, Cilt: 65 Sayı: 2, 121 - 132, 01.08.2016
https://doi.org/10.1501/Commua1_0000000764

Öz

Kaynakça

  • T. Acar, A. Aral and I. Ra¸sa, The new forms of Voronovskaya’s theorem in weighted spaces, Positivity, 20 (1) (2016), 25-40.
  • A. Aral, E. Deniz and V. Gupta, On Modi…cation of the Szasz-Durrmeyer Operators, Sub- mitted. O. Agratini, On an approximation process of integral type, App. Math. and Comput., 236 (2014), 195–201.
  • O. Agratini, Kantorovich sequences associated to general approximation processes, Positivity, (4) (2015), 681-693.
  • P.L. Butzer, On the extensions of Bernstein polynomials to the in…nite interval, Proc. Amer. Math. Soc., 5 (1954), 547–553.
  • O. Do¼gru, On a certain family of linear positive operators. Turkish J. Math., 21 (4) (1997), 399.
  • A. D. Gadjiev, R. O. Efendiyev and E. Ibikli, On Korovkin type theorem in the space of locally integrable functions, Czech. Math. J., 53 (128) (2003), 45-53.
  • A. D. Gadzhiev, Theorems of the of P. P. Korovkin type theorems, Math. Zametki, 20 (5) (1976), 781-786; Math. Notes, 20 (5-6) (1976), 996-998 (English Translation).
  • S. G. Gal and H. Gonska, Grüss and Grüss-Voronovskaya-type estimates for some Bernstein- type polynomials of real and complex variables, arXiv: 1401.6824v1.
  • V. Gupta and G. C. Greubel, Moment Estimations of New Szász-Mirakyan-Durrmeyer Op- erators, Appl. Math. Comput. 271 (2015), 540–547.
  • V. Gupta and R. P. Pant, Rate of convergence for the modi…ed Szász Mirakyan operators on functions of bounded variation, J. Math. Anal. Appl., 233 (2) (1999), 476-483.
  • N. Ispir, On modi…ed Baskakov operators on weighted spaces, Turk. J. Math., 26 (3) (2001) 365.
  • A. Olgun, F. Ta¸sdelen and A. Erençin, A generalization of Jain’s operators, App. Math. and Comput., 266 (2015), 6–11.
  • G. C. Jain, Approximation of functions by a new class of linear operators, J. Austral. Math. Soc., 13 (3) (1972), 271-276.
  • O. Szasz, Generalization of S. Bernstein’s polynomials to the in…nite interval, J. of Research of the Nat. Bur. of Standards, 45 (1950), 239-245.
  • S. Tarabie, On Jain-Beta Linear Operators, Appl. Math. Inf. Sci., 6 (2) (2012), 213-216.
  • S. Umar and Q. Razi, Approximation of function by a generalized Szász operators, Commu- nications de la Fac. Sci. L’Univ D’Ankara, 34 (1985), 45-52.
  • Current address : Department of Mathematics, Faculty of Science and Arts, Kirikkale Univer- sity, 71450 Yahsihan, Kirikkale, Turkey
  • E-mail address : emredeniz--@hotmail.com
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Emre Denız Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 65 Sayı: 2

Kaynak Göster

APA Denız, E. (2016). Quantitative estimates for Jain-Kantorovich operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 121-132. https://doi.org/10.1501/Commua1_0000000764
AMA Denız E. Quantitative estimates for Jain-Kantorovich operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2016;65(2):121-132. doi:10.1501/Commua1_0000000764
Chicago Denız, Emre. “Quantitative Estimates for Jain-Kantorovich Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, sy. 2 (Ağustos 2016): 121-32. https://doi.org/10.1501/Commua1_0000000764.
EndNote Denız E (01 Ağustos 2016) Quantitative estimates for Jain-Kantorovich operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 2 121–132.
IEEE E. Denız, “Quantitative estimates for Jain-Kantorovich operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 65, sy. 2, ss. 121–132, 2016, doi: 10.1501/Commua1_0000000764.
ISNAD Denız, Emre. “Quantitative Estimates for Jain-Kantorovich Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/2 (Ağustos 2016), 121-132. https://doi.org/10.1501/Commua1_0000000764.
JAMA Denız E. Quantitative estimates for Jain-Kantorovich operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:121–132.
MLA Denız, Emre. “Quantitative Estimates for Jain-Kantorovich Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 65, sy. 2, 2016, ss. 121-32, doi:10.1501/Commua1_0000000764.
Vancouver Denız E. Quantitative estimates for Jain-Kantorovich operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(2):121-32.

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