Differential subordination related to conic sections

In this paper some problems of the theory of differential subordination are investigated in connection with conic domains. In particular, fundamental conditions for functions mapped the unit disk onto domains bounded by parabolas and hyperbolas are deduced.     

Ma jorization Results and Coefficients Bounds for a Class of Univalent Functions Asso ciated with Operator

In this paper we introduce a new general subclass n,g ∑ a,λ(A, B,α) of univalent func-tions related the known integral operator and differential operator. Some majorization re-sults for n,g ∑ a,λ(A, B, 1) as well as the other functions are given. Furthermore, we find the coefficients bounds on|a2|and|a3|for functions in?n,g ∑ a,λ(A1, B1, A2, B2,α1,α2), which is the bi-univalent functions defined by n,g ∑ a,λ(A, B,α) and subordination. By giving specific values of the parameters of our main results, several(known or new) consequences of main results are also discussed.     

Convex and alpha-prestarlike subordination chains

In this paper we consider convex subordination chains (c.s.c.) and alpha-prestarlike subordination chains (α-p.s.c.) over (0,1] on the unit disc in the complex plane. We obtain sufficient conditions for a mapping f(z,t) to be an α-p.s.c. over (0,1], which generalize a well-known result of Ruscheweyh [St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l'Université de Montreal, 1982]. We also obtain sufficient conditions for injectivity for nonanalytic mappings on the unit disc, and give certain examples of α-c.s.c. over (0,1] on the unit disc.     

研究生录取问题的优化模型与评述

针对2004年首届全国部分高校研究生数学建模竞赛的D题“研究生录取”问题的评卷情况,概括地介绍了这个问题的背景、评卷要点、答卷中存在的问题.并且给出了这个问题的一种有效的解决方法.     

两个负系数P叶函数族的Hadamard积

给出了两个具有负系数P叶函数族Tp^*(A，B)与C，(A，B)的Hadamard积的若干性质．     

某类多叶解析函数的性质

设A(p)(p是指数，p≥1）表示在单位圆盘E内形如f(z)=z^p ap 1z^p 1…的解析函数族。本文引进了新的函数子类Hσ（p,α），找出了Hσ（p,α）闭凸包的极值点并给出精确的系数估计，还讨论了Hσ（p,α）其它一些有趣的性质。     

A rotation method which gives linear estimates for powers of the Ahlfors–Beurling operator

In [O. Dragičević, A. Volberg, Sharp estimate of the Ahlfors–Beurling operator via averaging martingale transforms, Michigan Math. J. 51 (2) (2003) 415–435] the Ahlfors–Beurling operator T was represented as an average of two-dimensional martingale transforms. The same result can be proven for powers Tⁿ. Motivated by [T. Iwaniec, G. Martin, Riesz transforms and related singular integrals, J. Reine Angew. Math. 473 (1996) 25–57], we deduce from here that Tⁿ_p are bounded from above by Cnp^*, . We further improve this estimate to obtain the optimal behaviour of the L^p norms in question.     

On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points

In the present paper, the authors introduce two new subclasses of close-to-convex functions and of quasi-convex functions. The integral representations for functions belonging to these classes are provided, the convolution conditions, growth theorems, distortion theorems and covering theorems for these classes are also provided. The results obtained generalize some known results, and some other new results are obtained.     

Strong Differential Subordination and Superordination Properties of Phi-Like Functions

Strong differential subordination and superordination properties are determined for Phi-like functions in the open unit disk by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.