Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses
For a function <i>p</i> analytic in the open unit disc and satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mn>0</mn><mo>...
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| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2879 |
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| author | Aaisha Farzana Habibullah Muthusamy Palani Jeyaraman Teodor Bulboacă |
| author_facet | Aaisha Farzana Habibullah Muthusamy Palani Jeyaraman Teodor Bulboacă |
| author_sort | Aaisha Farzana Habibullah |
| collection | DOAJ |
| description | For a function <i>p</i> analytic in the open unit disc and satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we prove certain subordination implications of the first order differential subordination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>z</mi><msup><mi>p</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>≺</mo><mn>1</mn><mo>+</mo><mi>M</mi><mi>z</mi></mrow></semantics></math></inline-formula>, which provides sufficient conditions for a function to belong to various subclasses of Ma-Minda starlike functions. The pre-Schwarzian norm estimate and inclusion criteria for certain subclasses of analytic function are also obtained. Additionally, using Gronwall’s inequality we give a sufficient condition for a normalized function to belong to a class of functions with bounded arguments that extends the class of strongly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Bazilevič functions of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> studied by Gao in 1996. |
| first_indexed | 2024-03-09T04:08:34Z |
| format | Article |
| id | doaj.art-4696707a2bdf43f594cda003a81efd7f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:08:34Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4696707a2bdf43f594cda003a81efd7f2023-12-03T14:03:09ZengMDPI AGMathematics2227-73902022-08-011016287910.3390/math10162879Subordinations and Norm Estimates for Functions Associated with Ma-Minda SubclassesAaisha Farzana Habibullah0Muthusamy Palani Jeyaraman1Teodor Bulboacă2Department of Mathematics with Computer Applications, A. M. Jain College, Meenambakkam, Chennai 600061, Tamil Nadu, IndiaDepartment of Mathematics, L. N. Government College, Ponneri, Chennai 601204, Tamil Nadu, IndiaFaculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaFor a function <i>p</i> analytic in the open unit disc and satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we prove certain subordination implications of the first order differential subordination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>z</mi><msup><mi>p</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>≺</mo><mn>1</mn><mo>+</mo><mi>M</mi><mi>z</mi></mrow></semantics></math></inline-formula>, which provides sufficient conditions for a function to belong to various subclasses of Ma-Minda starlike functions. The pre-Schwarzian norm estimate and inclusion criteria for certain subclasses of analytic function are also obtained. Additionally, using Gronwall’s inequality we give a sufficient condition for a normalized function to belong to a class of functions with bounded arguments that extends the class of strongly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Bazilevič functions of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> studied by Gao in 1996.https://www.mdpi.com/2227-7390/10/16/2879starlikeconvex and close-to-convex functionsdifferential subordinationnorm estimateSchwarzian derivativepre-Schwarzian derivative |
| spellingShingle | Aaisha Farzana Habibullah Muthusamy Palani Jeyaraman Teodor Bulboacă Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses Mathematics starlike convex and close-to-convex functions differential subordination norm estimate Schwarzian derivative pre-Schwarzian derivative |
| title | Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses |
| title_full | Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses |
| title_fullStr | Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses |
| title_full_unstemmed | Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses |
| title_short | Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses |
| title_sort | subordinations and norm estimates for functions associated with ma minda subclasses |
| topic | starlike convex and close-to-convex functions differential subordination norm estimate Schwarzian derivative pre-Schwarzian derivative |
| url | https://www.mdpi.com/2227-7390/10/16/2879 |
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