Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 23 Sayı: 4, 549 - 553, 01.08.2019
https://doi.org/10.16984/saufenbilder.484564

Öz

Kaynakça

  • acar1 : T. Acar, A. Aral and I. Raşa, Modified Bernstein-Durrmeyer operators, General Mathematics, 22 (1) (2014) 27-41.
  • gulsum : T. Acar, G. Ulusoy, Approximation by modified Szasz Durrmeyer operators, Period Math Hung, 72 (2016) 64-75.
  • baskakov : V. Baskakov, An instance of a sequence of linear positive operators in the space of continuous functions, Doklady Akademii Nauk SSSR 113 (2) (1957) 249-251.
  • acar2 : T. Acar, V. Gupta and A. Aral, Rate of Convergence for Generalized Szász Operators, Bulletin of Mathematical Science 1 (1) (2011) 99-113.
  • aral1 : A. Aral, D. Inoan and I. Raşa, On the Generalized Szász-Mirakyan Operators, Results in Mathematics 65 (2014) 441-452.
  • aral2 : A. Aral, V. Gupta, Generalized Szász Durrmeyer Operators, Lobachevskii J. Math. 32 (1) (2011) 23--31.
  • cardenes : D. Cárdenas-Morales, P. Garrancho, I. Raşa, Bernstein-type operators which preserve polynomials, Computers and Mathematics with Applications 62 (2011) 158-163.
  • gadziev1 : A. D. Gadziev, The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogues to that of P. P. Korovkin, Dokl. Akad. Nauk SSSR, 218 (1974) 1001-1004. Also in Soviet Math Dokl.15 (1974), 1433-1436 (in English).
  • gadziev2 : A. D. Gadziev, Theorems of the type of P. P. Korovkin's theorems (in Russian), Math. Z. 205 (1976), 781-786 translated in Math. Notes, 20 (5-6) (1977), 995-998.
  • gupta1 : V. Gupta, U. Abel, On the rate of convergence of Bézier variant of Szász-Durrmeyer operators, Anal. Theory Appl. 19 (1) (2003) 81-88.
  • holhos : A. Holhos, Quantitative estimates for positive linear operators in weighted space, General Math. 16 (4) (2008) 99-110.
  • mediha : Prashantkumar Patel, Vishnu Narayan Mishra and Mediha Örkcü, Some approximation properties of the generalized Baskakov operators, Journal of Interdisciplinary Mathematics, 21 (3) (2018) 611-622.

On the Generalized Baskakov Durrmeyer Operators

Yıl 2019, Cilt: 23 Sayı: 4, 549 - 553, 01.08.2019
https://doi.org/10.16984/saufenbilder.484564

Öz

The main object of this paper is to construct Baskakov Durrmeyer type operators such that their construction depends on a function ρ. Using the weighted modulus of continuity, we show the uniform convergence of the operators. Moreover we obtain pointwise convergence of B_{n}^{ρ} by obtaining Voronovskaya type theorem. All results show that our new operators are sensitive to the rate of convergence to f, depending on our selection of ρ.

Kaynakça

  • acar1 : T. Acar, A. Aral and I. Raşa, Modified Bernstein-Durrmeyer operators, General Mathematics, 22 (1) (2014) 27-41.
  • gulsum : T. Acar, G. Ulusoy, Approximation by modified Szasz Durrmeyer operators, Period Math Hung, 72 (2016) 64-75.
  • baskakov : V. Baskakov, An instance of a sequence of linear positive operators in the space of continuous functions, Doklady Akademii Nauk SSSR 113 (2) (1957) 249-251.
  • acar2 : T. Acar, V. Gupta and A. Aral, Rate of Convergence for Generalized Szász Operators, Bulletin of Mathematical Science 1 (1) (2011) 99-113.
  • aral1 : A. Aral, D. Inoan and I. Raşa, On the Generalized Szász-Mirakyan Operators, Results in Mathematics 65 (2014) 441-452.
  • aral2 : A. Aral, V. Gupta, Generalized Szász Durrmeyer Operators, Lobachevskii J. Math. 32 (1) (2011) 23--31.
  • cardenes : D. Cárdenas-Morales, P. Garrancho, I. Raşa, Bernstein-type operators which preserve polynomials, Computers and Mathematics with Applications 62 (2011) 158-163.
  • gadziev1 : A. D. Gadziev, The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogues to that of P. P. Korovkin, Dokl. Akad. Nauk SSSR, 218 (1974) 1001-1004. Also in Soviet Math Dokl.15 (1974), 1433-1436 (in English).
  • gadziev2 : A. D. Gadziev, Theorems of the type of P. P. Korovkin's theorems (in Russian), Math. Z. 205 (1976), 781-786 translated in Math. Notes, 20 (5-6) (1977), 995-998.
  • gupta1 : V. Gupta, U. Abel, On the rate of convergence of Bézier variant of Szász-Durrmeyer operators, Anal. Theory Appl. 19 (1) (2003) 81-88.
  • holhos : A. Holhos, Quantitative estimates for positive linear operators in weighted space, General Math. 16 (4) (2008) 99-110.
  • mediha : Prashantkumar Patel, Vishnu Narayan Mishra and Mediha Örkcü, Some approximation properties of the generalized Baskakov operators, Journal of Interdisciplinary Mathematics, 21 (3) (2018) 611-622.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Gülsüm Ulusoy 0000-0003-2755-2334

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 17 Kasım 2018
Kabul Tarihi 14 Ocak 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 23 Sayı: 4

Kaynak Göster

APA Ulusoy, G. (2019). On the Generalized Baskakov Durrmeyer Operators. Sakarya University Journal of Science, 23(4), 549-553. https://doi.org/10.16984/saufenbilder.484564
AMA Ulusoy G. On the Generalized Baskakov Durrmeyer Operators. SAUJS. Ağustos 2019;23(4):549-553. doi:10.16984/saufenbilder.484564
Chicago Ulusoy, Gülsüm. “On the Generalized Baskakov Durrmeyer Operators”. Sakarya University Journal of Science 23, sy. 4 (Ağustos 2019): 549-53. https://doi.org/10.16984/saufenbilder.484564.
EndNote Ulusoy G (01 Ağustos 2019) On the Generalized Baskakov Durrmeyer Operators. Sakarya University Journal of Science 23 4 549–553.
IEEE G. Ulusoy, “On the Generalized Baskakov Durrmeyer Operators”, SAUJS, c. 23, sy. 4, ss. 549–553, 2019, doi: 10.16984/saufenbilder.484564.
ISNAD Ulusoy, Gülsüm. “On the Generalized Baskakov Durrmeyer Operators”. Sakarya University Journal of Science 23/4 (Ağustos 2019), 549-553. https://doi.org/10.16984/saufenbilder.484564.
JAMA Ulusoy G. On the Generalized Baskakov Durrmeyer Operators. SAUJS. 2019;23:549–553.
MLA Ulusoy, Gülsüm. “On the Generalized Baskakov Durrmeyer Operators”. Sakarya University Journal of Science, c. 23, sy. 4, 2019, ss. 549-53, doi:10.16984/saufenbilder.484564.
Vancouver Ulusoy G. On the Generalized Baskakov Durrmeyer Operators. SAUJS. 2019;23(4):549-53.

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