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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117128400048X |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |