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Yıl 2021, Cilt: 70 Sayı: 1, 541 - 554, 30.06.2021

Kenan Bozkurt Fırat Özsaraç Ali Aral

https://doi.org/10.31801/cfsuasmas.793968
Cited By: 6

Öz

Kaynakça

  • Adell, J.A., De La Cal, J., San Miguel, M., On the property of monotonic convergence for multivariate Bernstein-type operators, J. Approx. Theory., 80 (1995), 132–137. https://doi.org/10.1006/jath.1995.1008
  • Aral, A., Acar, T., Ozsarac, F., Differentiated Bernstein type operators, Dolomites Research Notes on Approximation., 13 (1) (2020), 47-54. https://doi.org/10.14658/PUPJ-DRNA-2020-1-6
  • Aral, A., C´ardenas-Morales, D., Garrancho, P., Bernstein-type operators that reproduce exponential functions, J. of Math. Ineq., 12 (3) (2018), 861-872. https://doi.org/10.7153/jmi-2018-12-64
  • Aral, A., Limmam, M. L., Ozsarac, F., Approximation properties of Szász-Mirakyan-Kantorovich type operators, Math. Meth. Appl. Sci., 42 (16) (2018), 5233-5240. https://doi.org/10.1002/mma.5280
  • Bodur, M., Yilmaz, O. G., Aral, A., Approximation by Baskakov-Szász-Stancu operators preserving exponential function, Constr. Math. Anal., 1 (1) (2018), 1–8. https://doi.org/10.33205/cma.450708
  • Blaga, P., Catinaş, T., Coman, Gh., Bernstein-type operators on triangle with one curved side. Mediterr. J. Math., 9 (4) (2012), 843–855. https://doi.org/10.1007/s00009-011-0156-2
  • Blaga, P., Catinaş, T., Coman, Gh., Bernstein-type operators on a triangle with all curved sides, Applied Mathematics and Computation., 218 (2011), 3072–3082. https://doi.org/10.1016/j.amc.2011.08.027
  • Cárdenas-Morales, D., Garrancho, P., Munoz-Delgado, F.J., Shape preserving approximation by Bernstein-type operators which fix polynomials, Appl. Math. Comput., 182 (2) (2006), 1615–1622. https://doi.org/10.1016/j.amc.2006.05.046
  • Cárdenas-Morales, D., Munoz-Delgado, F.J., Improving certain Bernstein-type approximation processes, Math. and Comp. in Simulation., 77 (2008), 170-178. https://doi.org/10. 1016/j.matcom.2007.08.009
  • Censor, E., Quantitative results for positive linear approximation operators, J. Approx. Theory., 4 (1971), 442–450. https://doi.org/10.1016/0021-9045(71)90009-8
  • Ditzian, Z., Inverse theorems for multidimensional Bernstein operators, Pac. J. Math., 121 (2) (1986), 293–319. https://doi.org/10.2140/pjm.1986.121.293
  • Karlin, S., Studden, W.J., Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966. https://doi.org/10.1137/1009050
  • King, J.P., Positive linear operators which preserve x^2, Acta Math. Hungar., 99 (3) (2003), 203–208. https://doi.org/10.1023/A:1024571126455
  • Ozsarac, F., Acar, T., Reconstruction of Baskakov operators preserving some exponential functions, Math. Meth. Appl. Sci., 42 (16) (2018), 5124-5132. https://doi.org/10.1002/ mma.5228
  • Ozsarac, F., Aral, A., Karsli, H., On Bernstein–Chlodowsky type operators preserving exponential functions, Mathematical Analysis I: Approximation Theory-Springer., (2018), 121-138. https://doi.org/10.1007/978-981-15-1153-0_11

Bivariate Bernstein polynomials that reproduce exponential functions

Yıl 2021, Cilt: 70 Sayı: 1, 541 - 554, 30.06.2021

Kenan Bozkurt Fırat Özsaraç Ali Aral

https://doi.org/10.31801/cfsuasmas.793968
Cited By: 6

Öz

In this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters α and β not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.

Anahtar Kelimeler

Bernstein operators exponential functions classical and exponential convexity Voronovskaya-type theorem

Kaynakça

  • Adell, J.A., De La Cal, J., San Miguel, M., On the property of monotonic convergence for multivariate Bernstein-type operators, J. Approx. Theory., 80 (1995), 132–137. https://doi.org/10.1006/jath.1995.1008
  • Aral, A., Acar, T., Ozsarac, F., Differentiated Bernstein type operators, Dolomites Research Notes on Approximation., 13 (1) (2020), 47-54. https://doi.org/10.14658/PUPJ-DRNA-2020-1-6
  • Aral, A., C´ardenas-Morales, D., Garrancho, P., Bernstein-type operators that reproduce exponential functions, J. of Math. Ineq., 12 (3) (2018), 861-872. https://doi.org/10.7153/jmi-2018-12-64
  • Aral, A., Limmam, M. L., Ozsarac, F., Approximation properties of Szász-Mirakyan-Kantorovich type operators, Math. Meth. Appl. Sci., 42 (16) (2018), 5233-5240. https://doi.org/10.1002/mma.5280
  • Bodur, M., Yilmaz, O. G., Aral, A., Approximation by Baskakov-Szász-Stancu operators preserving exponential function, Constr. Math. Anal., 1 (1) (2018), 1–8. https://doi.org/10.33205/cma.450708
  • Blaga, P., Catinaş, T., Coman, Gh., Bernstein-type operators on triangle with one curved side. Mediterr. J. Math., 9 (4) (2012), 843–855. https://doi.org/10.1007/s00009-011-0156-2
  • Blaga, P., Catinaş, T., Coman, Gh., Bernstein-type operators on a triangle with all curved sides, Applied Mathematics and Computation., 218 (2011), 3072–3082. https://doi.org/10.1016/j.amc.2011.08.027
  • Cárdenas-Morales, D., Garrancho, P., Munoz-Delgado, F.J., Shape preserving approximation by Bernstein-type operators which fix polynomials, Appl. Math. Comput., 182 (2) (2006), 1615–1622. https://doi.org/10.1016/j.amc.2006.05.046
  • Cárdenas-Morales, D., Munoz-Delgado, F.J., Improving certain Bernstein-type approximation processes, Math. and Comp. in Simulation., 77 (2008), 170-178. https://doi.org/10. 1016/j.matcom.2007.08.009
  • Censor, E., Quantitative results for positive linear approximation operators, J. Approx. Theory., 4 (1971), 442–450. https://doi.org/10.1016/0021-9045(71)90009-8
  • Ditzian, Z., Inverse theorems for multidimensional Bernstein operators, Pac. J. Math., 121 (2) (1986), 293–319. https://doi.org/10.2140/pjm.1986.121.293
  • Karlin, S., Studden, W.J., Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966. https://doi.org/10.1137/1009050
  • King, J.P., Positive linear operators which preserve x^2, Acta Math. Hungar., 99 (3) (2003), 203–208. https://doi.org/10.1023/A:1024571126455
  • Ozsarac, F., Acar, T., Reconstruction of Baskakov operators preserving some exponential functions, Math. Meth. Appl. Sci., 42 (16) (2018), 5124-5132. https://doi.org/10.1002/ mma.5228
  • Ozsarac, F., Aral, A., Karsli, H., On Bernstein–Chlodowsky type operators preserving exponential functions, Mathematical Analysis I: Approximation Theory-Springer., (2018), 121-138. https://doi.org/10.1007/978-981-15-1153-0_11
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Kenan Bozkurt Bu kişi benim 0000-0001-9714-4729

Fırat Özsaraç 0000-0001-7170-9613

Ali Aral 0000-0002-2024-8607

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 12 Eylül 2020
Kabul Tarihi 2 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Bozkurt, K., Özsaraç, F., & Aral, A. (2021). Bivariate Bernstein polynomials that reproduce exponential functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 541-554. https://doi.org/10.31801/cfsuasmas.793968
AMA Bozkurt K, Özsaraç F, Aral A. Bivariate Bernstein polynomials that reproduce exponential functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):541-554. doi:10.31801/cfsuasmas.793968
Chicago Bozkurt, Kenan, Fırat Özsaraç, ve Ali Aral. “Bivariate Bernstein Polynomials That Reproduce Exponential Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 541-54. https://doi.org/10.31801/cfsuasmas.793968.
EndNote Bozkurt K, Özsaraç F, Aral A (01 Haziran 2021) Bivariate Bernstein polynomials that reproduce exponential functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 541–554.
IEEE K. Bozkurt, F. Özsaraç, ve A. Aral, “Bivariate Bernstein polynomials that reproduce exponential functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 541–554, 2021, doi: 10.31801/cfsuasmas.793968.
ISNAD Bozkurt, Kenan vd. “Bivariate Bernstein Polynomials That Reproduce Exponential Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 541-554. https://doi.org/10.31801/cfsuasmas.793968.
JAMA Bozkurt K, Özsaraç F, Aral A. Bivariate Bernstein polynomials that reproduce exponential functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:541–554.
MLA Bozkurt, Kenan vd. “Bivariate Bernstein Polynomials That Reproduce Exponential Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 541-54, doi:10.31801/cfsuasmas.793968.
Vancouver Bozkurt K, Özsaraç F, Aral A. Bivariate Bernstein polynomials that reproduce exponential functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):541-54.

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