Covering and distortion theorems for spirallike functions with respect to a boundary point

Covering results and perturbed Roper--Suffridge operators

This work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct perturbed extension operators in a certain class of Banach spaces and prove that these operators preserve the spirallikeness property. In addition, we present an extension operator for semigroup generators. We use a new geometric approach based on the connection between spirallike mappings and one-parameter continuous semigroups. It turns out that the new o…

Distortion and covering theorems of pluriharmonic mappings

In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

Coefficient, Distortion and Growth Inequalities for Certain Close-to-Convex Functions

In the present investigation, certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szegö functional for functions belonging to the class, distortion, growth estimates and covering theorems.

四元数上的切片星形函数

Slice starlike functions over quaternions

本文研究四元数上的切片星形函数及其子类，证明 Bieberbach 猜想成立，并建立精确的增长、畸变与覆盖定理。

($α,β$)-调和函数的性质

Properties for ($α,β$)-harmonic functions

本文研究($α,β$)-调和函数的系数估计、Heinz不等式、正交函数类及面积定理，通过$ L^p $范数分析边界函数的生长和扭曲估计。

Stable classes of harmonic mappings

Let $\mathcal{H}_0$ denote the set of all sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\ID$, normalized with $h(0)=g(0)=g'(0)=0$ and $h'(0)=1$. In this paper, we investigate some properties of certain subclasses of $\mathcal{H}_0$, including inclusion relations and stability analysis by precise examples, coefficient bounds, growth, covering and distortion theorems. As applications, we build some Bohr inequalities for these subclasses by means of subordination. Among these subclasses, six classes consist of functions $f=h+\overline{g}\in\mathcal{H}_0$ such that $h+εg$…