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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2006年第1期322卷 97-106页

作者： Wang, Zhi-Gang Gao, Chun-Yi Yuan, Shao-Mou Changsha Univ Sci & Technol Coll Math & Comp Sci Changsha 410076 Hunan Peoples R China

In the present paper, the authors introduce two new subclasses S-s((k)) (phi) of close-to-convex functions and C-s((k)) (phi) 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. (c) 2005 Elsevier Inc. All rights reserved.

关键词： close-to-convex functions quasi-convex functions differential subordination Hadamard product (or convolution) k-symmetric points

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Geometric properties of solutions of a class of ordinary linear differential equations

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期187卷 408-416页

作者： Saltoh, Hitoshi Gunma Natl Coll Technol Dept Math Gunma 3718530 Japan

The main object of this paper is to investigate several geometric properties of the solutions of the following second-order linear differential equation: w"(z) +p(z)w(z) = 0, where the function p(z) is analytic in the open unit disk U. Relevant connections of the results presented in this paper with those given earlier by, for example, Robertson, Miller and Saitoh are also considered. (C) 2006 Published by Elsevier Inc.

关键词： starlike functions strongly starlike functions close-to-convex functions differential equations univalent function

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On certain sufficient conditions for close-to-convexity

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期187卷 369-378页

作者： Patel, J. Cho, N. E. Utkal Univ Dept Math Bhubaneswar 751004 Orissa India Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

In this paper, we derive certain sufficient conditions for close-to-convexity of analytic functions by using the techniques of differential subordinations. Relevant connections of the results presented here with those... 详细信息

关键词： analytic functions p-valent functions hypergeometric function close-to-convex functions subordination between analytic functions

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Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2007年第1期331卷 686-700页

作者： Srivastava, H. M. Xu, N-Eng Yang, Ding-Gong Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada Changshu Inst Technol Dept Math Changshu 215500 Jiangsu Peoples R China Suzhou Univ Dept Math Suzhou 215006 Jiangsu Peoples R China

Let A denote the class of functions f (z) with f (0) = f'(0) - 1 = 0, which are analytic in the open unit disk U. By means of the Ruscheweyh derivatives, we introduce and investigate the various properties and characteristics of a certain two-parameter subclass T(alpha, lambda;h) of A, where alpha >= 0, lambda > -1, and h(z) is analytic and convex univalent in U with h(0) = 1. In particular, some inclusion relations and convolution properties for the function class T(alpha, lambda;h) are presented here. (C) 2006 Elsevier Inc. All rights reserved.

关键词： analytic functions convex functions univalent functions close-to-convex functions Hadamard product (or convolution) subordination between analytic functions Ruscheweyh derivatives

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Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators

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INTEGRAL TRANSFORMS AND SPECIAL functions 2007年第9期18卷 639-651页

作者： Prajapat, J. K. Raina, R. K. Srivastava, H. M. Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada Sobhasaria Engn Coll Dept Math Sikar 332001 Rajasthan India

A known family of fractional integral operators ( with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order beta and type alpha in the open unit disk U. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

关键词： analytic functions starlike functions convex functions close-to-convex functions strongly starlike functions strongly convex functions gauss hypergeometric function fractional integral operators inclusion properties

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The punishing factors for convex pairs are 2^n-1

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REVISTA MATEMATICA IBEROAMERICANA 2007年第3期23卷 847-860页

作者： Avkhadiev, Farit G. Wirths, Karl-Joachim Kazan VI Lenin State Univ Chebotarev Res Inst Kazan 420008 Russia Tech Univ Carolo Wilhelmina Braunschweig Inst Anal & Algebra D-38106 Braunschweig Germany

Let Omega and Pi be two simply connected proper subdomains of the complex plane C. We are concerned with the set A(Omega, Pi) of functions f : Omega -> Pi holomorphic on Omega and we prove estimates for vertical bar f((n))(z)vertical bar,f epsilon A(Omega,Pi),z epsilon Omega, of the following type. Let lambda(Omega)(z) and lambda(Pi)(w) denote the density of the Poincare metric with curvature K = -4 of Omega at z and of Pi at w, respectively. Then for any pair (Omega, Pi) of convex domains, f epsilon A(Omega, Pi), z epsilon Omega, and n >= 2 the inequality

关键词： convex domain linear accessible domain Taylor coefficients convex functions close-to-convex functions inverse functions bounded functions

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Bieberbach's conjecture, the de Branges and Weinstein functions and the Askey-Gasper inequality

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RAMANUJAN JOURNAL 2007年第1-3期13卷 103-129页

作者： Koepf, Wolfram Univ Kassel Dept Math D-34132 Kassel Germany

The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [4]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [5] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [2] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [72] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

关键词： Bieberbach conjecture Robertson conjecture Milin conjecture convex functions starlike functions close-to-convex functions Grunsky inequalities Schiffer variation support points extreme points Loewner differential equation Loewner theory Lebedev-Milin inequalities de Branges theorem de Branges functions Weinstein functions hypergeometric functions generalized hypergeometric series Askey-Gasper inequality Askey-Gasper identity Legendre addition theorem FPS algorithm Zeilberger algorithm maple symbolic computation computer algebra

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On the successive coefficients of close-to-convex functions

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2003年第2期283卷 689-695页

作者： Ye, ZQ JiangXi Norm Univ Dept Math Nanchang 30027 Peoples R China

Let f is an element of S, f be a close-to-convex function, f(k) (z) = [f (z(k))](1/k). The relative growth of successive coefficients of f(k) (z) is investigated. The sharp estimate of parallel toc(n+1)\ - \c(n)parall... 详细信息

关键词： successive coefficients close-to-convex functions subordination function

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Construction of a certain class of harmonic close-to-convex functions associated with the Alexander integral transform

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INTEGRAL TRANSFORMS AND SPECIAL functions 2003年第3期14卷 237-242页

作者： Jahangiri, JM Kim, YC Srivastava, HM Kent State Univ Dept Math & Comp Sci Burton OH 44021 USA Yeungnam Univ Dept Math Coll Educ Kyongsan 712749 South Korea Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada

The authors make use of the Alexander integral transforms of certain analytic functions (which are starlike or convex of positive order) with a view to investigating the construction of sense-preserving, univalent, an... 详细信息

关键词： Alexander integral transform analytic functions starlike functions convex functions close-to-convex functions harmonic functions

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The Hardy space for a certain subclass of Bazilevic functions

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期183卷 1201-1207页

作者： Kim, Yong Chan Srivastava, H. M. Univ Victoria Dept Math & Stat Victoria BC V8W 3P4 Canada Yeungnam Univ Dept Math Educ Gyongsan 712749 South Korea

In the present sequel to a recent paper by Kim and Sugawa [Y.C. Kim, T. Sugawa, Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions, Proc. Edinburgh Math. Soc. (Ser. 2) 49 (2006) 131-143], the authors introduce and investigate a general class of Bazilevic functions, which is defined by using the principle of subordination between analytic functions. They also determine the Hardy space to which this subclass of Bazilevic functions belongs under various parametric constraints. (c) 2006 Elsevier Inc. All rights reserved.

关键词： Hardy space Bazilevic functions close-to-convex functions starlike functions convex functions subordination between analytic functions

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