arXiv subjects

Yue-Ping Jiang

Publications and source records attributed to Yue-Ping Jiang.

3 recordsLinked to original sources

arXiv2020

Construction of univalent harmonic mappings convex in one direction

In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The results presented here provide extensions and improvements of those given in some earlier works. Several examples of univalent harmonic mappings convex in one direction are also constructed to demonstrate the main results.

math.CV↗

arXiv2013

Generators of Eisenstein--Picard modular group in three complex dimensions

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein--Picard modular group $\mathbf{PU}(3,1;\mathbb{Z}[ω_3])$ in three complex dimensions can be generated by four given transformations.

math.CV↗

arXiv2012

Inequalities for generalized trigonometric and hyperbolic sine functions

We prove that the inequalities $\sin_{p,q}(\sqrt{rs})\geq \sqrt{\sin_{p,q}(r)\sin_{p,q}(s)}$ and $\sinh_{p,q}(\sqrt{r^*s^*}) \leq \sqrt{\sinh_{p,q}(r^*)\sinh_{p,q}(s^*)}$ hold for all $p,q\in(1,\infty)$, $r,s\in(0,\int_{0}^{1}(1-t^q)^{-1/p}dt)$ and $r^*,s^*\in(0,\int_{0}^{\infty}(1+t^q)^{-1/p}dt)$, where $\sin_{p,q}$ and $\sinh_{p,q}$ are the generalized trigonometric and hyperbolic sine functions, respectively. As a consequence of the results, we prove a conjecture due to Bhayo and Vuorinen [J. Approx. Theory, 164(2012)].

math.CA↗