On the Strong Starlikeness of the Bernardi Transform
Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions <i>g</i>, such that <inline-formula><math...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/1/91 |
| Summary: | Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions <i>g</i>, such that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>|</mo><mo form="prefix">arg</mo></mrow><mrow><mo>{</mo><msup><mi>g</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>}</mo></mrow><mrow><mo>|</mo><mo> </mo><mo><</mo></mrow><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mi>α</mi><mi>π</mi></mrow><mn>2</mn></mfrac></mstyle></mrow></semantics></math></inline-formula> in the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Our results include the results of Mocanu, Nunokawa and others on the Libera transform. |
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| ISSN: | 2075-1680 |