Loading [a11y]/accessibility-menu.js
Research Article
BibTex RIS Cite

On difference of bivariate linear positive operators

Year 2022, Volume: 71 Issue: 3, 791 - 805, 30.09.2022
https://doi.org/10.31801/cfsuasmas.992524

Abstract

In the present paper we give quantitative type theorems for the differences of different bivariate positive linear operators by using weighted modulus of continuity. Similar estimates are obtained via K-functional and for Chebyshev functionals. Moreover, an example involving Szasz and Szasz-Kantorovich operators is given.

References

  • Acu, A. M., Raşa, I., New estimates for the differences of positive linear operators, Numer. Algor., 73(3) (2016), 775–789. https://doi.org/10.1007/s11075-016-0117-8
  • Acu, A. M., Hodiş, S., Raşa, I., A survey on estimates for the differences of positive linear operators, Constructive Mathematical Analysis, (1)2 (2018), 113–127. https://doi.org/10.33205/cma.478408
  • Acu, A. M., Raşa, I., Estimates for the differences of positive linear operators and their derivatives, Numer. Algor., 85(1) (2020), 191–208. https://doi.org/10.1007/s11075-019-00809-4
  • Acu, A. M., Başcanbaz-Tunca, G., Raşa, I., Differences of positive linear operators on simplices, Journal of Function Spaces, 2021 (2021), Article ID 5531577, 11 pages. https://doi.org/10.1155/2021/ 5531577
  • Aral, A., Inoan, D., Raşa, I., On differences of linear positive operators, Analysis and Mathematical Physics, (9)3 (2019), 1227–1239. https://doi.org/10.1007/s13324-018-0227-7
  • Aral, A., Erbay, H., A note on the difference of positive operators and numerical aspects, Mediterr. J. Math., 17(45) (2020), 20 pp. https://doi.org/10.1007/s00009-020-1489-5
  • Bartle, R. G., The Elements of Real Analysis, John Wiley & Sons Ltd, 1964.
  • Begen, S., Ince Ilarslan, H. G., Degree of approximation for bivariate Szazs-Kantorovich type based on Brenke type polynomials, Honam Math. J., (2020), 42(2), 251–268. https://doi.org/10.5831/HMJ.2020.42.2.251
  • Butzer, P. L., Berens, H., Semi-Groups of Operators and Approximation, Springer, New York, 1967.
  • Gadjieva, E., Doğru, O., Szasz Tipinde Operatörler Dizisinin Sürekli Fonksiyonlara Yaklaşımı, II. Uluslararası Kızılırmak Fen Bilimleri Kongresi, May 20-22, 1998.
  • Gonska, H., Pitul, P., Raşa, I., On differences of positive linear operators, Carpathian J. Math., 22(1-2) (2006), 65-78. https://www.jstor.org/stable/43998909
  • İşpir, N., Atakut, C., Approximation by modified Szasz-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112(4) (2002), 571–578. https://doi.org/10.1007/BF02829690
Year 2022, Volume: 71 Issue: 3, 791 - 805, 30.09.2022
https://doi.org/10.31801/cfsuasmas.992524

Abstract

References

  • Acu, A. M., Raşa, I., New estimates for the differences of positive linear operators, Numer. Algor., 73(3) (2016), 775–789. https://doi.org/10.1007/s11075-016-0117-8
  • Acu, A. M., Hodiş, S., Raşa, I., A survey on estimates for the differences of positive linear operators, Constructive Mathematical Analysis, (1)2 (2018), 113–127. https://doi.org/10.33205/cma.478408
  • Acu, A. M., Raşa, I., Estimates for the differences of positive linear operators and their derivatives, Numer. Algor., 85(1) (2020), 191–208. https://doi.org/10.1007/s11075-019-00809-4
  • Acu, A. M., Başcanbaz-Tunca, G., Raşa, I., Differences of positive linear operators on simplices, Journal of Function Spaces, 2021 (2021), Article ID 5531577, 11 pages. https://doi.org/10.1155/2021/ 5531577
  • Aral, A., Inoan, D., Raşa, I., On differences of linear positive operators, Analysis and Mathematical Physics, (9)3 (2019), 1227–1239. https://doi.org/10.1007/s13324-018-0227-7
  • Aral, A., Erbay, H., A note on the difference of positive operators and numerical aspects, Mediterr. J. Math., 17(45) (2020), 20 pp. https://doi.org/10.1007/s00009-020-1489-5
  • Bartle, R. G., The Elements of Real Analysis, John Wiley & Sons Ltd, 1964.
  • Begen, S., Ince Ilarslan, H. G., Degree of approximation for bivariate Szazs-Kantorovich type based on Brenke type polynomials, Honam Math. J., (2020), 42(2), 251–268. https://doi.org/10.5831/HMJ.2020.42.2.251
  • Butzer, P. L., Berens, H., Semi-Groups of Operators and Approximation, Springer, New York, 1967.
  • Gadjieva, E., Doğru, O., Szasz Tipinde Operatörler Dizisinin Sürekli Fonksiyonlara Yaklaşımı, II. Uluslararası Kızılırmak Fen Bilimleri Kongresi, May 20-22, 1998.
  • Gonska, H., Pitul, P., Raşa, I., On differences of positive linear operators, Carpathian J. Math., 22(1-2) (2006), 65-78. https://www.jstor.org/stable/43998909
  • İşpir, N., Atakut, C., Approximation by modified Szasz-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112(4) (2002), 571–578. https://doi.org/10.1007/BF02829690
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Saheed Olaosebikan Aremu 0000-0002-7016-5885

Ali Olgun 0000-0001-5365-4110

Publication Date September 30, 2022
Submission Date September 7, 2021
Acceptance Date January 31, 2022
Published in Issue Year 2022 Volume: 71 Issue: 3

Cite

APA Aremu, S. O., & Olgun, A. (2022). On difference of bivariate linear positive operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(3), 791-805. https://doi.org/10.31801/cfsuasmas.992524
AMA Aremu SO, Olgun A. On difference of bivariate linear positive operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. September 2022;71(3):791-805. doi:10.31801/cfsuasmas.992524
Chicago Aremu, Saheed Olaosebikan, and Ali Olgun. “On Difference of Bivariate Linear Positive Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 3 (September 2022): 791-805. https://doi.org/10.31801/cfsuasmas.992524.
EndNote Aremu SO, Olgun A (September 1, 2022) On difference of bivariate linear positive operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 3 791–805.
IEEE S. O. Aremu and A. Olgun, “On difference of bivariate linear positive operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 3, pp. 791–805, 2022, doi: 10.31801/cfsuasmas.992524.
ISNAD Aremu, Saheed Olaosebikan - Olgun, Ali. “On Difference of Bivariate Linear Positive Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/3 (September 2022), 791-805. https://doi.org/10.31801/cfsuasmas.992524.
JAMA Aremu SO, Olgun A. On difference of bivariate linear positive operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:791–805.
MLA Aremu, Saheed Olaosebikan and Ali Olgun. “On Difference of Bivariate Linear Positive Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 3, 2022, pp. 791-05, doi:10.31801/cfsuasmas.992524.
Vancouver Aremu SO, Olgun A. On difference of bivariate linear positive operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(3):791-805.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.