Sharp Initial Coefficient Bounds and the Fekete–Szegő Problem for Some Subclasses of Analytic and Bi-Univalent Functions

We introduce two new subclasses U Σ ( α , λ ) and ℬ 1Σ (α) of analytic bi-univalent functions defined in an open unit disk 𝕌, which are associated with the Bazilevich functions. In addition, for functions from these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients a 2...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 75; no. 2; pp. 225 - 234
Main Authors Patil, A. B., Shaba, T. G.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2023
Springer
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Statistics
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Summary:We introduce two new subclasses U Σ ( α , λ ) and ℬ 1Σ (α) of analytic bi-univalent functions defined in an open unit disk 𝕌, which are associated with the Bazilevich functions. In addition, for functions from these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients a 2 and a 3 , as well as the sharp estimate for the Fekete–Szegő functional a 3 - μ a 2 2 .
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-023-02195-6