Affiliation:
1. Mersin University, Faculty of Science and Letters, Department of Mathematics, Mersin, Turkey
Abstract
In this paper, we have introduced a Stancu generalization of the Szasz-Mirakyan-Bernstein Operators defined on the space of continuous functions defined on a compact interval. We have given a general formula for the moments of that operators. We have used Korovkin's Theorem for uniform approximation under some restrictions. We have obtained some results for the approximation rates in terms of modulus of continuity. Finally, we gave some Voronovskaya-type theorems.
Publisher
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
Reference12 articles.
1. Atakut, C., & Büyükyazici, I. (2010). Stancu type generalization of the Favard-Szasz operators. Applied Mathematics Letters, 23(12), 1479–1482. https://doi.org/10.1016/j.aml.2010.08.017
2. Bernstein, S.N. (1912). Demonstration du theoreme de Weierstrass fondee sur le calcul des probabilites. Communications of the Kharkov Mathematical Society, 13(1), 1–2.
3. Ciupa, A. (1994). On a generalized Favard-Szasz type operator. In Research Seminar on Numerical and Statistical Calculus, Univ. Babes Bolyai Cluj-Napoca, 1, 33–38.
4. Cleciu, V.A. (2007). Bernstein-Stancu operators. Stud. Univ. Babes-Bolyai, Math, 52, 53–65.
5. Devdhara, A.R., & Mishra, V.N. (2018). Local approximation results for Stancu variant of modified Szasz-Mirakjan operators. European Journal of Pure and Applied Mathematics, 11(2), 400–409. https://doi.org/10.29020/nybg.ejpam.v11i2.3214