A unified approach to radius of convexity problems for certain classes of univalent analytic functions
We consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier es...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128400048X |
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| _version_ | 1832566412725452800 |
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| author | M. L. Mogra O. P. Juneja |
| author_facet | M. L. Mogra O. P. Juneja |
| author_sort | M. L. Mogra |
| collection | DOAJ |
| description | We consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n+1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper. |
| format | Article |
| id | doaj-art-783067e26a5b40669fe07397053df517 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-783067e26a5b40669fe07397053df5172025-02-03T01:04:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017344345410.1155/S016117128400048XA unified approach to radius of convexity problems for certain classes of univalent analytic functionsM. L. Mogra0O. P. Juneja1School of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum, SudanDepartment of Mathematics, Indian Institute of Technology, Kanpur 208016, IndiaWe consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n+1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper.http://dx.doi.org/10.1155/S016117128400048Xradius of convexityunivalent functionsstarlike functions of order α and type β(n+1)-fold symmetric functionsfunctions with positive real part. |
| spellingShingle | M. L. Mogra O. P. Juneja A unified approach to radius of convexity problems for certain classes of univalent analytic functions International Journal of Mathematics and Mathematical Sciences radius of convexity univalent functions starlike functions of order α and type β (n+1)-fold symmetric functions functions with positive real part. |
| title | A unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| title_full | A unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| title_fullStr | A unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| title_full_unstemmed | A unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| title_short | A unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| title_sort | unified approach to radius of convexity problems for certain classes of univalent analytic functions |
| topic | radius of convexity univalent functions starlike functions of order α and type β (n+1)-fold symmetric functions functions with positive real part. |
| url | http://dx.doi.org/10.1155/S016117128400048X |
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