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The Goluzin Problem of Univalent Functions

Author: LiuWenJun
Tutor: YeZhongQiu
School: Jiangxi Normal University
Course: Basic mathematics
Keywords: Univalent function Adjacent coefficients Starlike functions Nearly convex function
CLC: O174.5
Type: Master's thesis
Year: 2003
Downloads: 21
Quote: 0
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Abstract


Univalent functions on the central issue is the coefficient , while the the adjacent coefficient mold difference between Goluzin problem is both difficult and interesting problems unresolved . Professor Hu Ke made ??a series of studies on this issue for nearly convex function symmetric function K times to get answers to your questions . This paper study univalent functions Goluzin problem . First of all, nearly convex function S c extended to the larger function the family S c ( α ) : Let f (z) ∈ S , α is a real number , there is g (z) ∈ S * , so | Z | < 1 established, we Vocabulary S c (α) , f (z) satisfies the above conditions composed the family of functions . When α = 1 , it is clear that f ∈ S c is the S c ( 1 ) = S c S easy to know c (α) (?) S c . Then, the integrated use of the basics of univalent functions , such as positive real part function family Hergloz said the theorem , area principle , Goluzin inequality , , Milin-Lebjev inequality the Milin theorem , Schwarz inequality , integration by parts , univalent functions mold nature , such as through a number of new integral estimation method to obtain the about S c ( α ) family function the adjacent coefficient model accurately estimated Theorem : Let f k ( z ) = [f (z k )] 1 / k = z sum from n = 1 to ∞ (a n 1 k < / sup> z kn 1 ∈ Sc (α), is where A α < / sub > is the only constant with α -order 1/k-1 best . this theorem is Professor Hu Ke paper [1] on close to the adjacent convex function coefficients an important theorem promotion and strengthened .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Complex analysis,complex function
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