TY - JOUR T1 - On difference of bivariate linear positive operators AU - Olgun, Ali AU - Aremu, Saheed Olaosebikan PY - 2022 DA - September Y2 - 2022 DO - 10.31801/cfsuasmas.992524 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 791 EP - 805 VL - 71 IS - 3 LA - en AB - 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. KW - Chebyshev functionals KW - bivariate positive linear operators KW - weighted modulus of continuity CR - 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 CR - 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 CR - 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 CR - 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 CR - 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 CR - 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 CR - Bartle, R. G., The Elements of Real Analysis, John Wiley & Sons Ltd, 1964. CR - 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 CR - Butzer, P. L., Berens, H., Semi-Groups of Operators and Approximation, Springer, New York, 1967. CR - Gadjieva, E., Doğru, O., Szasz Tipinde Operatörler Dizisinin Sürekli Fonksiyonlara Yaklaşımı, II. Uluslararası Kızılırmak Fen Bilimleri Kongresi, May 20-22, 1998. CR - 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 CR - 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 UR - https://doi.org/10.31801/cfsuasmas.992524 L1 - https://dergipark.org.tr/en/download/article-file/1962638 ER -