Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions

Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions

Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">B</mi></semantics></math></inline-formula> denote the class of bounded turning functions <inline...

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Bibliographic Details
Main Authors:	Sudhansu Palei, Madan Mohan Soren, Luminiţa-Ioana Cotîrlǎ, Daniel Breaz
Format:	Article
Language:	English
Published:	MDPI AG 2025-06-01
Series:	Mathematics
Subjects:	analytic functions bounded turning functions coefficient bounds Fekete–Szegö-type inequality Hankel determinant Krushkal and Zalcman functional
Online Access:	https://www.mdpi.com/2227-7390/13/11/1845
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Summary:	Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">B</mi></semantics></math></inline-formula> denote the class of bounded turning functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula> analytic in the open unit disk, where the image of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">F</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is contained in the domain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Ω</mo><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>cosh</mi><mi>z</mi><mo>+</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mn>2</mn><mi>z</mi></mrow><mrow><mn>2</mn><mo>−</mo><msup><mi>z</mi><mn>2</mn></msup></mrow></mfrac></mstyle></mrow></semantics></math></inline-formula>. This article determines sharp coefficient bounds, a Fekete–Szegö-type inequality, and second- and third-order Hankel determinants for functions in the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">B</mi></semantics></math></inline-formula>. Additionally, we obtain sharp Krushkal and Zalcman functional-type inequalities related to the logarithmic coefficient for functions belonging to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">B</mi></semantics></math></inline-formula>.
ISSN:	2227-7390