Successive Logarithmic Coefficients of Univalent Functions

The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in the class S , where γ n ( f ) denotes the n -th logarithmic coefficient of f ∈ S . The result is applicable to some standard subclasses of S ....

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Vydáno v:Computational methods and function theory Ročník 24; číslo 4; s. 693 - 705
Hlavní autoři: Lecko, Adam, Partyka, Dariusz
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
Témata:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
30C75
30C45
30C50
Logarithmic coefficients
Univalent functions
Successive coefficients
ISSN:1617-9447, 2195-3724
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Abstract The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in the class S , where γ n ( f ) denotes the n -th logarithmic coefficient of f ∈ S . The result is applicable to some standard subclasses of S . Relevant examples were indicated.
AbstractList The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of $$|\gamma _2(f)|-|\gamma _1(f)|$$ | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in the class $${\mathcal {S}}$$ S , where $$\gamma _n(f)$$ γ n ( f ) denotes the n -th logarithmic coefficient of $$f\in {\mathcal {S}}$$ f ∈ S . The result is applicable to some standard subclasses of $${\mathcal {S}}$$ S . Relevant examples were indicated.
The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in the class S , where γ n ( f ) denotes the n -th logarithmic coefficient of f ∈ S . The result is applicable to some standard subclasses of S . Relevant examples were indicated.
Author Partyka, Dariusz
Lecko, Adam
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  givenname: Dariusz
  surname: Partyka
  fullname: Partyka, Dariusz
  organization: Department of Mathematical Analysis, The John Paul II Catholic University of Lublin, Institute of Mathematics and Information Technology, The University College of Applied Sciences in Chełm
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Cites_doi 10.1112/jlms/s1-38.1.228
10.2307/2370963
10.1090/proc/13817
10.1090/proc/12921
10.1307/mmj/1028988895
10.1007/BF02392821
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10.1007/s00605-017-1092-4
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Issue 4
Keywords 30C75
30C45
30C50
Logarithmic coefficients
Univalent functions
Successive coefficients
Language English
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PublicationTitle Computational methods and function theory
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Snippet The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in...
The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of $$|\gamma _2(f)|-|\gamma _1(f)|$$ | γ 2 ( f ) |...
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SubjectTerms Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Title Successive Logarithmic Coefficients of Univalent Functions
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