Results on Second-Order Hankel Determinants for Convex Functions with Symmetric Points

One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some sharp estimates of problems involvi...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 4; p. 939
Main Authors Ullah, Khalil, Al-Shbeil, Isra, Faisal, Muhammad, Arif, Muhammad, Alsaud, Huda
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2023
Subjects
Coefficients
convex functions with respect to symmetric points
Estimates
Hankel determinant problems
Hyperbolic functions
Inequality
logarithmic and inverse coefficients
MacLaurin series
Mathematical analysis
subordinations
Zalcman functionals
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Summary:One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some sharp estimates of problems involving coefficients for the family of convex functions with respect to symmetric points and associated with a hyperbolic tangent function. These problems include the first four initial coefficients, the Fekete–Szegö and Zalcman inequalities, and the second-order Hankel determinant. Additionally, the inverse and logarithmic coefficients of the functions belonging to the defined class are also studied in relation to the current problems.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15040939