Bernstein-Type Operators That Reproduce Exponential Functions
Künye
Aral, Ali & Cárdenas-Morales, D. & Garrancho, P.. (2018). Bernstein-type operators that reproduce exponential functions. Journal of Mathematical Inequalities. 12. 861-872.Özet
In this paper we recover a generalization of the classical Bernstein operators introduced by Morigi and Neamtu in 2000. Specifically, we focus on a sequence of operators that reproduce the exponential functions exp(mu t) and exp(2 mu t), mu > 0. We study its convergence, this including qualitative and quantitative theorems, an asymptotic formula and saturation results. We also show their shape preserving properties by considering generalized convexity. Finally, a comparison is stated, that shows that in a certain sense and for certain family of illustrative functions the new sequence approximates better than the classical Bernstein polynomials.
Kaynak
Journal Of Mathematical InequalitiesCilt
12Sayı
3Koleksiyonlar
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