Radius Results for Certain Strongly Starlike Functions
This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1124 |
| _version_ | 1797598215558660096 |
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| author | Afis Saliu Kanwal Jabeen Qin Xin Fairouz Tchier Sarfraz Nawaz Malik |
| author_facet | Afis Saliu Kanwal Jabeen Qin Xin Fairouz Tchier Sarfraz Nawaz Malik |
| author_sort | Afis Saliu |
| collection | DOAJ |
| description | This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">φ</mi></semantics></math></inline-formula> defined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">φ</mi><mrow><mo>(</mo><mi mathvariant="sans-serif">ζ</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi mathvariant="sans-serif">ζ</mi><mo>)</mo></mrow><mi mathvariant="sans-serif">λ</mi></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi mathvariant="sans-serif">λ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp. |
| first_indexed | 2024-03-11T03:16:12Z |
| format | Article |
| id | doaj.art-3abafd2369ba4223861e09419333c360 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:12Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3abafd2369ba4223861e09419333c3602023-11-18T03:31:16ZengMDPI AGSymmetry2073-89942023-05-01155112410.3390/sym15051124Radius Results for Certain Strongly Starlike FunctionsAfis Saliu0Kanwal Jabeen1Qin Xin2Fairouz Tchier3Sarfraz Nawaz Malik4Department of Mathematics, University of the Gambia, MDI Road, Kanifing, Serrekunda P.O. Box 3530, The GambiaBright Future International School, Doha P.O. Box 8884, QatarFaculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, DenmarkMathematics Department, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi ArabiaDepartment of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt 47040, PakistanThis article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">φ</mi></semantics></math></inline-formula> defined by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">φ</mi><mrow><mo>(</mo><mi mathvariant="sans-serif">ζ</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi mathvariant="sans-serif">ζ</mi><mo>)</mo></mrow><mi mathvariant="sans-serif">λ</mi></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi mathvariant="sans-serif">λ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp.https://www.mdpi.com/2073-8994/15/5/1124univalent functionsubordinationanalytic functionlemniscate of BernoulliSchwarz function |
| spellingShingle | Afis Saliu Kanwal Jabeen Qin Xin Fairouz Tchier Sarfraz Nawaz Malik Radius Results for Certain Strongly Starlike Functions Symmetry univalent function subordination analytic function lemniscate of Bernoulli Schwarz function |
| title | Radius Results for Certain Strongly Starlike Functions |
| title_full | Radius Results for Certain Strongly Starlike Functions |
| title_fullStr | Radius Results for Certain Strongly Starlike Functions |
| title_full_unstemmed | Radius Results for Certain Strongly Starlike Functions |
| title_short | Radius Results for Certain Strongly Starlike Functions |
| title_sort | radius results for certain strongly starlike functions |
| topic | univalent function subordination analytic function lemniscate of Bernoulli Schwarz function |
| url | https://www.mdpi.com/2073-8994/15/5/1124 |
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