1 citations · 3 across the 4 of their papers we have counts for
5 papers
A lower bound for the beta function
Tiehong Zhao, Miaokun Wang
We present a new lower bound for Euler's beta function, , which states that the inequality \begin{equation*} B(x,y)>\frac{x+y}{xy}\left(1-\frac{2xy}{x+y+1}\right) \end{equa…
A note on the Neuman-Sándor Mean
Tie-Hong Zhao, Yu-Ming Chu, Bao-Yu Liu
In this article, we present the best possible upper and lower bounds for the Neuman-Sándor mean in terms of the geometric combinations of harmonic and quadratic means, geometric an…
Some Best Possible Inequalities Concerning Certain Bivariate Means
Tie-Hong Zhao, Yu-Ming Chu, Bao-Yu Liu
In this paper, some inequalities of bounds for the Neuman-Sándor mean in terms of weighted arithmetic means of two bivariate means are established. Bounds involving weighted arithm…
Optimal bounds for the Neuman-Sandor means in terms of geometric and contra-harmonic means
Tie-Hong Zhao, Yu-Ming Chu, Bo-Yu Liu
In this article, we prove that the double inequality holds true for all with if and only if and $β\…
Generators for the Euclidean Picard Modular Groups
Tiehong Zhao
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Eu…