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Wei-Dong Jiang

Publications and source records attributed to Wei-Dong Jiang.

7 recordsLinked to original sources
arXiv2014

Bounds for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean

In the paper, the authors find the greatest value $λ$ and the least value $μ$ such that the double inequality \begin{multline*} C(λa+(1-λ)b,λb+(1-λ)a)<αA(a,b)+(1-α)T(a,b)\\ < C(μa+(1-μ)b,μb+(1-μ)a) \end{multline*} holds for all $α\in(0,1)$ and $a,b>0$ with $a\ne b$, where $$ C(a,b)=\frac{a^{2}+b^{2}}{a+b},\quad A(a,b)=\frac{a+b}2, $$ and $$ T(a,b)=\frac{2}π\int_{0}^{π/{2}}\sqrt{a^2\cos^2θ+b^2\sin^2θ}\,dθ$$ denote respectively the contraharmonic, arithmetic, and Toader means of two positive numbers $a$ and $b$.

math.CA↗
arXiv2013

Geometric convexity of the generalized sine and the generalized hyperbolic sine

In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively. Consequently, the authors verify a conjecture posed in the paper "B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at \url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".

math.CA↗
arXiv2012

Some sharp inequalities involving Seiffert and other means and their concise proofs

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers $a$ and $b$ with $a\ne b$.

math.CA↗