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In the article, we prove that the double inequalities Mα(a,b)<SQA(a,b)<Mβ(a,b)$M_{\alpha }(a,b)< S_{QA}(a,b)< M_{\beta}(a,b)$ and Mλ(a,b)<SAQ(a,b)<Mμ(a,b)$M_{\lambda }(a,b)< S_{AQ}(a,b)<… (More)

Using the series-expansion of digamma functions and other techniques, some monotonicity and logarithmical concavity involving the ratio of gamma function are obtained, which is to give a partially… (More)

We present the best possible lower and upper bounds for the Neuman-Sandor mean in terms of the convex combinations of either the harmonic and quadratic means or the geometric and quadratic means or… (More)

Abstract In this article, we prove that the double inequality
α P ( a , b ) + 1 ( 1 − α ) Q ( a , b ) M ( a , b ) β P ( a , b ) + ( 1 − β ) Q ( a , b ) holds for any a,b > 0 with a ≠ b if and only… (More)

- Tie-Hong Zhao, Yu-Ming Chu, Hua Wang
- 2011

monotonic on � 0, ∞� if � α, β� ∈{ � α, β� :1 / √ α ≤ β ≤ 1 ,α / 1 }∪{ � α, β� :0 <β ≤ 1 ,ϕ 1� α, β� ≥ 0 ,ϕ 2� α, β� ≥ 0} andfα,β� x�� −1 is strictly logarithmically completely monotonic on � 0, ∞�… (More)

- Tie-Hong Zhao, Yu-Ming Chu, Wen Zhang
- Journal of inequalities and applications
- 2017

AbstractIn this paper, we present the best possible parameters α(r)$\alpha(r)$ and β(r)$\beta(r)$ such that the double inequality
… (More)

In this paper, we present the best possible parameter a∈(1/15,∞)$a\in(1/15, \infty)$ such that the functions ψ′(x+1)−Lx(x,a)$\psi^{\prime}(x+1)-\mathcal{L}_{x}(x, a)$ and… (More)

In this paper, we present the best possible parameters p,q∈R$p, q\in\mathbb {R}$ such that the double inequality Mp(a,b)0$a, b>0$ with a≠b$a\neq b$, and we get sharp bounds for the complete elliptic… (More)

- Tie-Hong Zhao, Miao-Kun Wang, Wen Zhang, Y. Ralph Chu
- Journal of inequalities and applications
- 2018

In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring… (More)

- Yu-Ming Chu, Tie-Hong Zhao
- 2015

In this paper, the authors present necessary and sufficient conditions for the complete elliptic integrals of the first and second kind to be convex or concave with respect to the Lehmer mean.