Aral, AliCardenas-Morales, DanielGarrancho, Pedro2020-06-252020-06-252018Aral, Ali & Cárdenas-Morales, D. & Garrancho, P.. (2018). Bernstein-type operators that reproduce exponential functions. Journal of Mathematical Inequalities. 12. 861-872.1846-579Xhttps://doi.org/10.7153/jmi-2018-12-64https://hdl.handle.net/20.500.12587/7326Cardenas-Morales, Daniel/0000-0003-1038-3116In 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.eninfo:eu-repo/semantics/openAccessModified Bernstein-type operatorsexponential functionsshape preserving propertiesgeneralized convexityArticle12386187210.7153/jmi-2018-12-642-s2.0-85055540428Q2WOS:000445366500019Q1