A new approach to improve the order of approximation of the Bernstein operators: theory and applications |
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| Authors: | Hassan Khosravian-Arab Mehdi Dehghan M. R. Eslahchi |
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| Affiliation: | 1.Department of Applied Mathematics, Faculty of Mathematics Computer Sciences,Amirkabir University of Technology,Tehran,Iran;2.Department of Applied Mathematics, Faculty of Mathematical Sciences,Tarbiat Modares University,Tehran,Iran |
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| Abstract: | This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically. |
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