Abstract We prove that Bernstein operators preserve log-concavity of functions. We give a proof, which bases solely on elementary properties of the binomial coefficients. We prove that the Bernstein semigroup ( T ( t ) ) t ≥ 0 also has the log-concavity preserving property. We also solve two problems presented recently by I. Rasa.

中文翻译：

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Bernstein 算子和 Bernstein 半群的对数凹面保持性

摘要 我们证明了伯恩斯坦算子保持函数的对数凹度。我们给出了一个仅基于二项式系数的基本性质的证明。我们证明 Bernstein 半群 ( T ( t ) ) t ≥ 0 也具有对数凹面保持性。我们还解决了 I. Rasa 最近提出的两个问题。