Yue Ping Jiang

Bio: Yue Ping Jiang is an academic researcher from Hunan University. The author has contributed to research in topics: Convex combination & Convex function. The author has an hindex of 3, co-authored 3 publications receiving 29 citations.

Linear combinations of harmonic quasiconformal mappings convex in one direction

Abstract: In this paper, we introduce a new class $\mathscr{S}_{H} (k, γ; \phi)$ of harmonic quasiconformal mappings, where $k \in [0,1), γ \in [0,π)$ and $\phi$ is an analytic function. Sufficient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of $γ$ and $\phi$, are convex.

Integral Representations and Coefficient Estimates for a Subclass of Meromorphic Starlike Functions

Abstract: In this paper, we introduce a natural subclass of meromorphic starlike functions in the open unit disk. Results concerning subordination properties, integral representations, properties of convolutions, inclusion relationship and coefficient inequalities for the functions of this class are derived. Furthermore, we solve radius problems for certain related classes of meromorphic strongly starlike functions and meromorphic parabolic starlike functions.

On a subclass of close-to-convex harmonic mappings

Abstract: We introduce a new subclass of close-to-convex harmonic mappings in the unit disk, which originates from the work of P. Mocanu on univalent mappings. We also give coefficient estimates, and discuss the Fekete-Szegő problem, for this class of mappings. Furthermore, we consider growth, covering and area theorems of the class. In addition, we determine a disk in which the partial sum is close-to-convex for each function of the class . Finally, for certain values of the parameters and , we solve the radii problems related to starlikeness and convexity of functions of this class.

Bohr inequality for certain harmonic mappings

Abstract: Let $\phi$ be analytic and univalent ({\it i.e.,} one-to-one) in $\mathbb{D}:=\{z\in\mathbb{C}: |z| 0$. A function $f \in \mathcal{C}(\phi)$ if $1+ zf''(z)/f'(z) \prec \phi (z),$ and $f\in \mathcal{C}_{c}(\phi)$ if $2(zf'(z))'/(f(z)+\overline{f(\bar{z})})' \prec \phi (z)$ for $ z\in \mathbb{D}$. In this article, we consider the classes $\mathcal{HC}(\phi)$ and $\mathcal{HC}_{c}(\phi)$ consisting of harmonic mappings $f=h+\overline{g}$ of the form $$ h(z)=z+ \sum \limits_{n=2}^{\infty} a_{n}z^{n} \quad \mbox{and} \quad g(z)=\sum \limits_{n=2}^{\infty} b_{n}z^{n} $$ in the unit disk $\mathbb{D}$, where $h$ belongs to $\mathcal{C}(\phi)$ and $\mathcal{C}_{c}(\phi)$ respectively, with the dilation $g'(z)=\alpha z h'(z)$ and $|\alpha|<1$. Using the Bohr phenomenon for subordination classes \cite[Lemma 1]{bhowmik-2018}, we find the radius $R_{f}<1$ such that Bohr inequality $$ |z|+\sum_{n=2}^{\infty} (|a_{n}|+|b_{n}|)|z|^{n} \leq d(f(0),\partial f(\mathbb{D})) $$ holds for $|z|=r\leq R_{f}$ for the classes $\mathcal{HC}(\phi)$ and $\mathcal{HC}_{c}(\phi)$ . As a consequence of these results, we obtain several interesting corollaries on Bohr inequality for the aforesaid classes.

Hadamard products of certain classes of p -valent starlike functions

Abstract: In this paper, we consider several convolution properties for two subclasses of p-valent starlike functions.

Some Families of Analytic Functions in the Upper HalfPlane and Their Associated Differential Subordination and Differential Superordination Properties and Problems

Abstract: The existing literature in Geometric Function Theory of Com plex Analysis contains a considerably large number of interesting investigations dealing with differential sub ordination and differential superordination problems for analytic functions in the unit disk. Nevertheless, only a few of these earlier inve stigations deal with the above-mentioned problems in the up per half-plane. The notion of differential subordination in the upper halfplane was introduced by Răducanu and Pascu in [ 16]. For a setΩ in the complex planeC, let the functionp(z) be analytic in the upper half-plane ∆ given by ∆ = {z : z∈ C and I(z)> 0} and suppose that ψ : C3×∆ →C. The main object of this article is to consider the problem of determining properties of functions p(z) that satisfy the following differential superordination: Ω ⊂ { ψ ( p(z), p(z), p(z);z ) : z∈ ∆ } . We also present several applications of the results derived in this article to differential subordination and differen tial superordination for analytic functions in∆ .

On convex combinations of convex harmonic mappings

Abstract: The family of orientation-preserving harmonic functions in the unit disc (normalised in the standard way) satisfying for some , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in are convex.