On Stancu type Szász-Mirakyan-Durrmeyer Operators Preserving Exp(2ax), a>0

Year 2021, , 196 - 209, 01.03.2021

Kadir Kanat Melek Sofyalıoğlu

https://doi.org/10.35378/gujs.691419

Cited By: 5

Abstract

The present paper deals with the Szász-Mirakyan-Durrmeyer-Stancu operators preserving 𝑒2𝑎𝑥 for a>0. The uniform convergence of the constructed operators is mentioned in this paper. The rate of convergence is examined by employing two different modulus of continuities. After that, a Voronovskaya-type theorem is investigated for quantitative asymptotic estimation. Finally, a comparison is made theoretically to show that the new constructed operators perform well.

Keywords

Exponential functions, Voronovskaya-type theorem, Modulus of Continuity

References

• [1] Mazhar, S.M., Totik, V., “Approximation by modified Szász operators”, Acta Sci. Math., 49: 257-269, (1985).
• [2] Acar, T., Aral, A., Gonska, H., “On Szász-Mirakyan operators preserving e^2ax,a>0”, Mediterranean J. Math., 14(6): 1-14, (2017).
• [3] Deniz, E., Aral, A., Gupta, V., “Note on Szász-Mirakyan-Durrmeyer operators preserving e^2ax, a>0”, Numerical Functional Analysis and Optimization, 39(2): 201-207, (2018).
• [4] Gupta, V., Deo, N., Zeng, X., “Simultaneous Approximation for Szász-Mirakian-Stancu-Durrmeyer Operators”, Analysis in Theory and Applications, 29(1): 86-96, (2013).
• [5] Acar, T., Aral, A., Cárdenas-Morales, D., Garrancho, P., “Szász-Mirakyan Type Operators Which Fix Exponentials”, Results Math., 72: 1393-1404, (2017).
• [6] Aral, A., Inoan, D., Raşa, I., “Approximation properties of Szász-Mirakyan operators preserving exponential functions”, Positivity, 23: 233-246, (2019).
• [7] Bodur, M., Gürel Yılmaz, Ö., Aral, A., “Approximation by Baskakov-Szász-Stancu Operators Preserving Exponential Functions”, Constructive Mathematical Analysis, 1(1): 1-8, (2018).
• [8] Gupta, V., Acu, A.M., “On Baskakov-Szász-Mirakyan-type operators preserving exponential type functions”, Positivity, 22: 919-929, (2018).
• [9] Gupta, V., Aral, A., “A note on Szász-Mirakyan-Kantorovich type operators preserving e^(-x)”, Positivity, 22: 415-423, (2018).
• [10] Boyanov, B.D. and Veselinov, V.M., “A note on the approximation of functions in an infinite interval by linear positive operators”, Bull. Math. Soc. Sci. Math. Roum., 14(62): 9-13, (1970).
• [11] Holhoş, A., “The rate of approximation of functions in an infinite interval by positive linear operators”, Stud. Univ. Babes-Bolyai Math., 2: 133-142, (2010).
• [12] DeVore, RA., Lorentz, G.G., “Constructive Approximation”, Springer, Berlin, 177, (1993).
• [13] Tachev, G., Gupta, V., Aral, A., “Voronovskaja’s theorem for functions with exponential growth”, Georgian Mathematical Journal, (2018). doi:10.1515/gmj-2018-0041