C~N中多项式映照的周期点

本文研究到自身的多项式映照ｆ（ｚ）＝ｆ０（ｚ）＋ｆ１（ｚ）＋…＋ｆｋ（ｚ）的动力学，其中ｆｊ是ｆ的ｊ次齐次部分，其最高次项ｆｋ是非退化的，ｋ２．全文讨论了ｆ的不动点个数问题以及周期点的存在性问题．     

平均单叶函数的相邻系数

设ｆ（ｚ）＝ｚ＋Σａｎｚ＾ｎ为单位园｜ｚ｜＜１内解析且平均单叶，记其族为Ｍ又设｛ｆ（ｚ）／ｚ｝＾λ＝１＋Σ＾∞ｎ＝１Ｄｎ（λ），λ＞０，本文说明了：定理一 若ｆ∈Ｍ，λ＞０，则：Σ＾∞ｋ＝１｛｜｜Ｄｋ（λ）｜－｜Ｄｋ－１（λ）｜｜／ｄｋ（λ）｝＾２≤Ａｎ，ｎ＝２，３，…其中Ａ为绝对常数。ｄｋ（ｈ）＝ｈ（ｈ＋１）…（ｈ＋ｋ－１）／ｋ！当λ＝１／２，ｆ∈ｓ时为Ｉ．Ｖ．Ｍｉｌｍ所证明。定理二 若ｆ∈Ｍ并     

亚纯函数的幅角分布及其增长性

本文考虑了亚纯函数的幅角分布及其增长性的关系，得到了如下定理：设ｆ（ｚ）为亚纯函数，下级μ（μ〈＋∞，ａｒｇｚ＝θｋ（ｋ＝１，２，…，ｑ；０≤θ１〈θ２〈…〈θｑ〈２π，θｑ＋１＝θ１＋２π）为ｑ（１≤ｑ〈＋∞）条半直线使对Ａ↓ε〉０有：ｌｉｍｒ→∞↑－ｌｏｇ＋ｎ↑－（∪ｋ＝１↑ｑΩ↑－（θｋ＋ε，θｋ＋１－ε；ｒ），ｆ＝ｘ）／ｌｏｇｒ≤ρ〈＋∞ ｘ＝０，∞则当存在一非负整数ｌ使ｆ＾（ｌ）（ｚ）（     

多圆柱上正规化双全纯星形映照的齐次展式

本文讨论单位多圆柱△ｎ＝｛ｚ＝（ｚ１,ｚ２,…,ｚｙ ∈Ｃｎ：｜ｚ｜＝ｍａｘ ｜ｚｊ｜＜１｝上正规化双全 纯星形映照的表示形式．证明对这种映照ｆ的第ｊ个分量ｆｊ,有ｆｊ＝ｇｊｚｊ,（ｊ＝１,２,…,ｎ）,这里 （ｇ１,ｇ２,…,ｇｎ）＇为△ｎ上的全纯映照．     

关于Briot—Bouquet微分从属

本文主要研究如下的Ｂｒｉｏｔ－Ｂｏｕｑｕｅｔ微分从属Ｐ（Ｚ）＋ＺＰ＇（Ｚ）／βＰ（Ｚ）＋γ＜１＋ａｚ／１＋ｂｚ，ｐ（０）＝１其中ｐ在｜ｚ｜Ｄ＜１内解析，β、γ、ａ、ｂ为适当的实数，并由此解决了Ｓ．Ｓ．Ｍｉｌｌｅｒ和Ｐ．Ｔ．Ｍｏｃａｎｕ提出的一。     

象域为多边形的单叶调和映射

本文对于给定的Ｂｅｔｒａｍｉ系数ａ（ｚ）找到了存在将单位圆盘Ｕ映射为给定的多边形Ｐ并且满足方程ｆｘ＾－＝ａ（ｚ）ｆｘ的单叶调和保向映射函数ｆ（ｚ）的条件。     

星形函数族的一个子族的极值点与支撑点

设Ｆ（｛ｎ｝）＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥０，＋∞ｎ＝２ｎａｎ≤１｝，则Ｆ（｛ｎ｝）是星形函数族的一个子族．许多学者研究了这个函数族．设Ｍ＝｛ｆ（ｚ）：ｆ（ｚ）在｜ｚ｜＜１内解析，ｆ（ｚ）＝ｚ－∞ｎ＝１ａｎｚｎ，ａｎ≥ａｎ＋１≥０，＋∞ｎ＝２ｎａｎ≤１｝．在本文中我们找出了函数族Ｍ的极值点与支撑点．     

关于两类积分算子的性质

设ｆ（ｚ）＝ｚ＋ａ２ｚ＾２＋…在单位圆的Ｄ内解析，β，γ，ｃ为常数，γ≠０，定义积分虎子，Ｉ１（ｆ）（ｚ）＝∫＾ｚ０（ｆ（ｔ）／ｔ）βｄｔ，Ｉ（ｆ）（ｚ）＝「γ＋ｃ／ｚ＾ｃ∫＾ｚ０ｔ＾ｃ－１（ｆ（ｔ））γｄｔ」＾１／γ。讨论了积分算子Ｉ１与Ｉ２的一些性质，改进了有关这两类积分算子的几个结果。     

莫斯科大学数学力学系1996年入学考试试题

莫斯科大学数学力学系１９９６年入学考试试题试卷１（３月）１解方程ｌｏｇｘ＋５（ｘ３＋１０ｘ２＋２０ｘ）·ｌｏｇ３（ｘ＋５）＝ｌｏｇ３（３ｘ２＋８ｘ）．２解不等式ｘ３－８＋６ｘ（２－ｘ）｜３－４ｘ｜≤４ｘ－３．３含边ＡＢ＝４与∠Ａ＝６０°的△ＡＢＣ内接...     

由费马点引出的若干竞赛问题

费马点及其性质如果Ｆ为△ＡＢＣ的费马点,ａ、ｂ、ｃ和Ｓ分别为△ＡＢＣ的三条边长和面积,ＦＡ＝ｘ,ＦＢ＝ｙ,ＦＣ＝ｚ,ｆ＝ｘ＋ｙ＋ｚ（下同）,那么费马点Ｆ有下述性质：定理当△ＡＢＣ的三内角均小于１２０°时,ｆ＝２２ａ２＋ｂ２＋ｃ２＋４３Ｓ（１）当△ＡＢ...     

Generalized B-vex functions and generalized B-vex programming

A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319. The second author is grateful to the Faculty of Management, University of Manitoba for the financial support provided for her visit. The authors are thankful to Prof. R. N. Kaul, Department of Mathematics, Delhi University for his constructive criticism of the paper.     

复变函数中由调和函数求解析函数的方法

本文给出了由解析函数的实部或虚部求该解析函数的几个定理,再以例题说明其应用。这些方法及应用,解决了复变函数中这一问题的理论与计算,而且所给方法能广泛进行推广。     

Functional inequalities involving special functions

Let up(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let σ(r)=up(1−r²)/up(r²), r∈(0,1). Motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen we prove that for all r₁,r₂∈(0,1) for certain conditions on the parameters b,c,p.     

Indefinite integrals of products of special functions

A method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of the method are presented, which applies directly to functions which obey homogeneous differential equations. However, functions which obey inhomogeneous equations can be incorporated into the products and examples are given of integrals involving products of Bessel functions combined with Lommel, Anger and Weber functions. Many new integrals are derived for a selection of special functions, including Bessel functions, associated Legendre functions, and elliptic integrals. A number of integrals of products of Gauss hypergeometric functions are also presented, which seem to be the first integrals of this type. All results presented have been numerically checked with Mathematica.     

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g=f⁻¹ satisfying the conditions that zf^′(z)/f(z) and zg^′(z)/g(z) are both subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.     

On the extremality of maximal dual feasible functions

Dual feasible functions have been used to compute bounds and valid inequalities for combinatorial optimization problems. Here, we analyze the properties of some of the best functions proposed so far. Additionally, we provide new results for composed functions. These results will allow improving the computation of bounds and valid inequalities.     

SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.     

A note on hyperharmonic and polyharmonic functions

We show that the spaces of harmonic functions with respect to the Poincaré metric in the unit ball B^N in have many different properties depending upon whether N is even or odd.     

严格r-预不变凸函数

引入了严格r-预不变凸函数的概念,并证明了严格r-预不变凸函数与r-预不变凸函数有关的一个充分条件．同时,讨论得到了严格r-预不变凸性和半严格r-预不变凸性的等价条件．