Logarithmic convexity of Gini means
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
math.CA↗
arXiv subjects
Bai-Ni Guo
Publications and source records attributed to Bai-Ni Guo.
An alternative proof of Elezović-Giordano-Pečarić's theorem
In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezović, C. Giordano and J. Pečarić, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. Appl. \textbf{3} (2000), 239\nobreakdash--252.].
math.CA↗
Some properties of the psi and polygamma functions
In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
math.CA↗
A note on additivity of polygamma functions
In the note, the functions $\abs{ψ^{(i)}(e^x)}$ for $i\in\mathbb{N}$ are proved to be sub-additive on $(\lnθ_i,\infty)$ and super-additive on $(-\infty,\lnθ_i)$, where $θ_i\in(0,1)$ is the unique root of equation $2\abs{ψ^{(i)}(θ)}=\abs{ψ^{(i)}(θ^2)}$.
math.CA↗
Sharpening and generalizations of Shafer's inequality for the arc tangent function
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
math.CA↗
Sharpening and generalizations of Carlson's double inequality for the arc cosine function
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
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Sharp inequalities for the psi function and harmonic numbers
In this paper, two sharp inequalities for bounding the psi function $ψ$ and the harmonic numbers $H_n$ are established respectively, some results in [I. Muqattash and M. Yahdi, \textit{Infinite family of approximations of the Digamma function}, Math. Comput. Modelling \textbf{43} (2006), 1329\nobreakdash--1336.] are improved, and some remarks are given.
math.CA↗
Two new proofs of the complete monotonicity of a function involving the psi function
In the present paper, we give two new proofs for the necessary and sufficient condition $α\le1$ such that the function $x^α[\ln x-ψ(x)]$ is completely monotonic on $(0,\infty)$.
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A concise proof of Oppenheim's double inequality relating to the cosine and sine functions
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
math.CA↗