Feng Qi
Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 3 August 2014 pp 333-342
Some Hermite–Hadamard Type Inequalities for Geometrically Quasi-Convex Functions
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.
Volume 124 Issue 4 November 2014 pp 527-531
A double inequality for bounding Toader mean by the centroidal mean
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.
Volume 127 Issue 4 September 2017 pp 551-564 Research Article
Some inequalities for the Bell numbers
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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