On difference of bivariate linear positive operators

Year 2022, Volume: 71 Issue: 3, 791 - 805, 30.09.2022

Saheed Olaosebikan Aremu , Ali Olgun

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.

Keywords

Chebyshev functionals, bivariate positive linear operators, weighted modulus of continuity

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