一类解析函数族及其α阶组合问题

引进用 Hλ算子刻画的一族解析函数 Pn(λ,α,β,ρ)并研究族 Pn(λ,α,β,ρ)上算子函数及其导数的α阶组合问题 .得到用α阶组合定义的函数在圆域 |Z|相似文献   

三维双曲空间中平行曲面族的两个定理

设 M 是三维双曲空间 H~3中的光滑曲面,M 的两个主曲率为λ_1和λ_2.设{M_t}是 M的平行曲面族(-ε相似文献   

一些单叶函数族导数的积分平均值

K(α),st_k(α),C(β,α),(α<1,β<1)分别表示α阶凸函数族,k 次对称的α阶星形函数族,α型β阶的近于凸函数族.在这篇文章中,我们分別对(?)(K(α)的闭凸包),(?),(?),(α<1,β≤1/2)决定了凸泛函L(f)=(1/(2π)(?)))~(1/p),0≤r<1,p≥1,n=1,2,…,的极值和极值函数.我们的结果表明:极值函数仅依赖于函数族而与参数 n,r,p 无关;而且对任何固定的函数族,除掉旋转外极值函数是唯一的.     

关于β级预星象函数的子族的一个不等式

引进并;研究解析函数族J（λ,α,β）,发现J（λ,α,β）与β级星象函数族之间的一种新关系,并应用此关系及一阶微分从属证明关于实部的一个不等式,由此得到了β级α凸函数的新实部不等式。     

分担值与正规族

设F是平面区域D上的亚纯函数族,a,b是两个有穷非零复数.如果(A)f∈F,f(z)=a(=)f(k)(z)=a,f(k)(z)=b(=)f(k+1)(z)=b,且f-a的零点重数至少为k(k≥3),那么函数族F在D内正规;当k=2时,在条件a≠4b的情况下,同样有函数族F在D内正规.     

一类新的解析函数族

定义了一族解析函数B(λ,α,β),导出该族中函数的积分表达式;借助算子理论建立B(λ,α,β)的包含关系,讨论端点性质;由此推出族中函数的偏差定理.     

一类亚纯多叶星象函数的子族

本文研究了一类亚纯多叶星象函数的子族(?)_p(β,λ).利用分析的方法与技巧,得到了函数族(?)_p(β,λ)的系数估计、邻域与部分和性质及一些包含关系,所得结果推广了相关作者的一些成果.     

有关近于凸函数的一族解析函数

本文引进并研究D^λ算子定义的一族解析函数Bλ(α，β)．导出族中函数的积分表达式；得到该族与近于凸函数之间的关系并借助算子理论讨论了Bλ(α，β)的包含关系，端点性质；由此推出族中函数的偏差定理，证明一个系数不等式．     

一类亚纯多叶星象函数的子族（英文）

本文研究了一类亚纯多叶星象函数的子族(?)_p(β,λ).利用分析的方法与技巧,得到了函数族(?)_p(β,λ)的系数估计、邻域与部分和性质及一些包含关系,所得结果推广了相关作者的一些成果.     

关于β级的α+iμ型λ-Bazilevich函数的几个不等式

本文引进β级的α iμ型λ—Bazilevich函数并讨论其子族Bn(λ，α，μ，β)的不等式性质，运用微分从属方法得到了Re{(1-A)(f(z)/z)^α iμ λ(f′(z))^α iμ}的精确下界，其中f(z)∈Bn(λ，α，μ，β)，它推广或改进了一些作者的有关工作，同时得到相关结果。     

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.     

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.     

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.     

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.     

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.     

Theoretical investigations on maximal dual feasible functions

Dual feasible functions are used to get valid inequalities and lower bounds for integer linear problems. In this paper, we provide a simpler proof for maximality, and we describe new results concerning the extremality of functions from the literature. Extremal functions are a dominant class of dual feasible functions.