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.
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
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
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.