• Feng Qi

      Articles written in Proceedings – Mathematical Sciences

    • Some Hermite–Hadamard Type Inequalities for Geometrically Quasi-Convex Functions

      Feng Qi Bo-Yan Xi

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      In the paper, we introduce a new concept ‘geometrically quasi-convex function’ and establish some Hermite–Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.

    • A double inequality for bounding Toader mean by the centroidal mean

      Yun Hua Feng Qi

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      In this paper, the authors find the best numbers 𝛼 and 𝛽 such that $\overline{C}(\alpha a+ (1 - \alpha)b$, $\alpha b + (1 - \alpha)a) \lt T (a, b) \lt \overline{C} (\beta a + (1 - \beta)b, \beta b + (1 - \beta)a)$ for all 𝑎, $b \gt 0$ with $a \neq b$, where $\overline{C}(a, b) = \frac{2(a^{2}+ab+b^{2})}{3(a+b)}$ and $T(a, b) = \frac{2}{\pi} \int^{\pi/2}_{0}\sqrt{a^{2}\cos^{2}\theta + b^{2}\sin^{2} \theta} {\rm d}\theta$ denote respectively the centroidal mean and Toader mean of two positive numbers 𝑎 and 𝑏.

    • Some inequalities for the Bell numbers

      FENG QI

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      In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers.

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