On the Gakhov Equation for the Biernacki Operator
The paper establishes the region in the parameter plane such that the image of any starlike function with the zero root of the Gakhov equation under the mapping by the Biernacki operator corresponding to the parameter of this region is found in the Gakhov class consisting of the functions, for which...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2015-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/portal/docs/F_408568177/157_2_phys_mat_7.pdf |
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| _version_ | 1841563015771586560 |
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| author | A.V. Kazantsev |
| author_facet | A.V. Kazantsev |
| author_sort | A.V. Kazantsev |
| collection | DOAJ |
| description | The paper establishes the region in the parameter plane such that the image of any starlike function with the zero root of the Gakhov equation under the mapping by the Biernacki operator corresponding to the parameter of this region is found in the Gakhov class consisting of the functions, for which this root is unique. It is demonstrated that the above region cannot be extended without loss of the uniqueness of the root for the image of at least one starlike function. For the image of the whole class of starlike functions having the zero root, the Gakhov width is calculated and the effective description is given for the set of trajectories of the exit out of the Gakhov class along the level lines. |
| format | Article |
| id | doaj-art-af8651d5e6ed4b1398ec1bbdf96d8eb2 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-af8651d5e6ed4b1398ec1bbdf96d8eb22025-01-03T00:27:42ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-06-0115727992On the Gakhov Equation for the Biernacki OperatorA.V. Kazantsev0Kazan Federal University, Kazan, 420008 RussiaThe paper establishes the region in the parameter plane such that the image of any starlike function with the zero root of the Gakhov equation under the mapping by the Biernacki operator corresponding to the parameter of this region is found in the Gakhov class consisting of the functions, for which this root is unique. It is demonstrated that the above region cannot be extended without loss of the uniqueness of the root for the image of at least one starlike function. For the image of the whole class of starlike functions having the zero root, the Gakhov width is calculated and the effective description is given for the set of trajectories of the exit out of the Gakhov class along the level lines.https://kpfu.ru/portal/docs/F_408568177/157_2_phys_mat_7.pdfbiernacki operatorgakhov equationstarlike functionsgakhov classgakhov width |
| spellingShingle | A.V. Kazantsev On the Gakhov Equation for the Biernacki Operator Учёные записки Казанского университета: Серия Физико-математические науки biernacki operator gakhov equation starlike functions gakhov class gakhov width |
| title | On the Gakhov Equation for the Biernacki Operator |
| title_full | On the Gakhov Equation for the Biernacki Operator |
| title_fullStr | On the Gakhov Equation for the Biernacki Operator |
| title_full_unstemmed | On the Gakhov Equation for the Biernacki Operator |
| title_short | On the Gakhov Equation for the Biernacki Operator |
| title_sort | on the gakhov equation for the biernacki operator |
| topic | biernacki operator gakhov equation starlike functions gakhov class gakhov width |
| url | https://kpfu.ru/portal/docs/F_408568177/157_2_phys_mat_7.pdf |
| work_keys_str_mv | AT avkazantsev onthegakhovequationforthebiernackioperator |