Zhen-Hang Yang

Three families of two-parameter means constructed by trigonometric functions

In this paper, we establish three families of trigonometric functions with two parameters and prove their monotonicity and bivariate log-convexity. Based on them, three two-parameter families of means involving trigonometric functions, which include Schwab-Borchardt mean, the first and second Seiffert means, Sándor’s mean and many other new means, are defined. Their properties are given and some new inequalities for these means are proved. Lastly, two families of two-parameter hyperbolic means, which similarly contain many new means, are also presented without proofs.MSC: 26E60, 26D05, 33B10, 26A48.

On rational bounds for the gamma function

AbstractIn the article, we prove that the double inequality x2+p0x+p0<Γ(x+1)<x2+9/5x+9/5

On approximating the modified Bessel function of the second kind

\frac{x^{2}+p_{0}}{x+p_{0}}< \Gamma(x+1)< \frac{x^{2}+9/5}{x+9/5}

Complete monotonicity involving some ratios of gamma functions

holds for all x∈(0,1)

Monotonicity of the ratio of modified Bessel functions of the first kind with applications

x\in(0, 1)

Sharp Smith’s bounds for the gamma function

, we present the best possible constants λ and μ such that λ(x2+9/5)x+9/5≤Γ(x+1)≤μ(x2+p0)x+p0

Monotonicity of the incomplete gamma function with applications

\frac{\lambda(x^{2}+9/5)}{x+9/5}\leq\Gamma(x+1)\leq\frac{\mu (x^{2}+p_{0})}{x+p_{0}}