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本文研究了用Salagean算子定义的缺系数单叶调和函数类.利用从属关系和算子理论得到类中函数的系数估计、极值点、偏差定理、卷积性质、凸性组合与凸半径,推广了已有的一些结果. 相似文献
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A CLASS OF HARMONIC STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS ASSOCIATED WITH WRIGHT GENERALIZED HYPERGEOMETRIC FUNCTION
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Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination. 相似文献
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A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points. 相似文献
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《Mathematische Nachrichten》2018,291(10):1502-1513
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem. 相似文献
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本文主要讨论了带限制条件的正实部解析函数族及纯凸像函数族的一般极值问题.首先我们得了两类带限制条件的正实部函数族的支撑点的表达式.其次,我们讨论了亚纯凸像函数族的极值问题,得到了亚纯凸像函数族上Frchet可导泛函所对应的极函数的最好形式. 相似文献
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借用著名的Ruscheweyh导数,引入了一类单叶保向调和函数族. 通过建立极值理论,得到了关联该族的最优系数边界、最优增长定理和最优偏差定理. 同时,给出了该族与先前已有调和函数族之间的转换半径. 最后,讨论了基于该族的修正哈达玛乘积结果. 相似文献
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We refine and generalize a result of V. A. Zmorovich on the integral representation of a class of univalent functions which are convex in some direction. We prove that all function of the class being considered can be approximated by a Schwarz-Christoffel integral of a special form belonging to the same class.Translated from Matematicheskii Zametki, Vol. 19, No. 1, pp. 41–48, January, 1976. 相似文献
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We study the integral operator $P_\lambda |f|(\zeta ) = \int {_{\zeta _0 }^\zeta } \left( {f\prime \left( t \right)} \right)^\lambda dt,{\text{ }}|\zeta |{\text{ }} > 1$ , acting on the class ∑ of functions meromorphic and univalent in the exterior of the unit disk. We refine the ranges of the parameter λ for which the operator preserves univalence either on ∑ or on its subclasses consisting of convex functions. As a consequence, a two-sided estimate is deduced for the separating constant in the sufficient condition for the univalent solvability of exterior inverse boundary-value problems. 相似文献
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In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ■≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm■. 相似文献
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Peter Duren 《Journal of Mathematical Analysis and Applications》2005,307(1):312-320
A general version of the Radó-Kneser-Choquet theorem implies that a piecewise constant sense-preserving mapping of the unit circle onto the vertices of a convex polygon extends to a univalent harmonic mapping of the unit disk onto the polygonal domain. This paper discusses similarly generated harmonic mappings of the disk onto nonconvex polygonal regions in the shape of regular stars. Calculation of the Blaschke product dilatation allows a determination of the exact range of parameters that produce univalent mappings. 相似文献
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《Applied Mathematics Letters》2003,16(6):905-909
Ruscheweyh and Sheil-Small proved the PólyarSchoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that close-to-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve close-to-convexity under convolution. An auxiliary function enables us to obtain necessary and sufficient convolution conditions for convex and starlike harmonic functions, which lead to sufficient coefficient bounds for inclusion in these classes. 相似文献
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In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates. 相似文献
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《复变函数与椭圆型方程》2012,57(2):81-92
Functions f in the class $ K_H $ are convex, univalent, harmonic, and sense preserving in the unit disk. Such functions can be expressed as $ f = h + \overline {g} $ where h and g are analytic functions. If $ f \in K_H $ has $ h(0) = 0, g(0) = 0, h'(0) = 1$ , and $ g'(0) = 0 $ , then $ f \in K_H^0 $ . For $ f \in K_H^0 $ and } analytic in the unit disk, an integral representation for $ f\tilde {*}\varphi = h*\varphi + \overline {g*\varphi } $ is found. With } a strip mapping, $ f\tilde {*}\varphi $ is shown to be in $ K_H^0 $ . In a 1958 paper, Pólya and Schoenberg conjectured that if f and g are conformal mappings of the unit disk onto convex domains, then the Hadamard product f 2 g of f and g has the same property. It is known that the analogue of that result for harmonic mappings is false. In this paper, some examples are given in which the property of convexity is preserved for Hadamard products of certain convex harmonic mappings. In addition, an integral formula is used to determine the geometry of the Hadamard product from the geometry of the factors. This is true in particular for the convolution of strip mappings with certain functions $ f_n \in K_H^0 $ which take the unit disk to regular n -gons. 相似文献
15.
Michael Dorff 《Proceedings of the American Mathematical Society》2004,132(2):491-498
Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust's theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent analytic mappings, this family of convolution surfaces is much larger than just the family of associated surfaces. Also, this generalization guarantees that all the resulting surfaces are over close-to-convex domains. In particular, all the associate surfaces and certain Goursat transformation surfaces of a minimal graph over a convex domain are over close-to-convex domains.
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本文讨论了Hilbert空间中具有正算子系数的亚纯单叶算子值函数集Σ[α,β],得到了f(z)∈Σ[α,β]的充要条件及算子系数估计,并表明在算术平均及凸线性组合下Σ[α,β]是闭的. 相似文献
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In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi-type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions. 相似文献
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Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity. 相似文献