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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2025-06-01
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| author | Sudhansu Palei Madan Mohan Soren Luminiţa-Ioana Cotîrlǎ Daniel Breaz |
| author_facet | Sudhansu Palei Madan Mohan Soren Luminiţa-Ioana Cotîrlǎ Daniel Breaz |
| author_sort | Sudhansu Palei |
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| description | 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>. |
| format | Article |
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| institution | Kabale University |
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| publishDate | 2025-06-01 |
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| spelling | doaj-art-bb2152c358084a4faa38f17fec8c6ef42025-08-20T03:46:45ZengMDPI AGMathematics2227-73902025-06-011311184510.3390/math13111845Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning FunctionsSudhansu Palei0Madan Mohan Soren1Luminiţa-Ioana Cotîrlǎ2Daniel Breaz3Department of Mathematics, Berhampur University, Berhampur 760007, Odisha, IndiaDepartment of Mathematics, Berhampur University, Berhampur 760007, Odisha, IndiaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaDepartment of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaLet <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>.https://www.mdpi.com/2227-7390/13/11/1845analytic functionsbounded turning functionscoefficient boundsFekete–Szegö-type inequalityHankel determinantKrushkal and Zalcman functional |
| spellingShingle | Sudhansu Palei Madan Mohan Soren Luminiţa-Ioana Cotîrlǎ Daniel Breaz Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions Mathematics analytic functions bounded turning functions coefficient bounds Fekete–Szegö-type inequality Hankel determinant Krushkal and Zalcman functional |
| title | Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions |
| title_full | Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions |
| title_fullStr | Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions |
| title_full_unstemmed | Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions |
| title_short | Sharp Coefficient Bounds for Analytic Functions Related to Bounded Turning Functions |
| title_sort | sharp coefficient bounds for analytic functions related to bounded turning functions |
| topic | analytic functions bounded turning functions coefficient bounds Fekete–Szegö-type inequality Hankel determinant Krushkal and Zalcman functional |
| url | https://www.mdpi.com/2227-7390/13/11/1845 |
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