The radius of convexity of certain analytic functions II
In [2], MacGregor found the radius of convexity of the functions f(z)=z+a2z2+a3z3+…, analytic and univalent such that |f′(z)−1|<1. This paper generalized MacGregor's theorem, by considering another univalent function g(z)=z+b2z2+b3z3+… such that |f′(z)g′(z)−1|<1 for |z|<1. Several theo...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000361 |
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| _version_ | 1832566182218039296 |
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| author | J. S. Ratti |
| author_facet | J. S. Ratti |
| author_sort | J. S. Ratti |
| collection | DOAJ |
| description | In [2], MacGregor found the radius of convexity of the functions f(z)=z+a2z2+a3z3+…, analytic and univalent such that |f′(z)−1|<1. This paper generalized MacGregor's theorem, by considering another univalent function g(z)=z+b2z2+b3z3+… such that |f′(z)g′(z)−1|<1 for |z|<1. Several theorems are proved with sharp results for the radius of convexity of the subfamilies of functions associated with the cases: g(z) is starlike for |z|<1, g(z) is convex for |z|<1, Re{g′(z)}>α(α=0,1/2). |
| format | Article |
| id | doaj-art-15f9e061b5c24f7fa965e21347f822b2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-15f9e061b5c24f7fa965e21347f822b22025-02-03T01:04:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013348348910.1155/S0161171280000361The radius of convexity of certain analytic functions IIJ. S. Ratti0Department of Mathematics, University of South Florida, Tampa 33620, Florida, USAIn [2], MacGregor found the radius of convexity of the functions f(z)=z+a2z2+a3z3+…, analytic and univalent such that |f′(z)−1|<1. This paper generalized MacGregor's theorem, by considering another univalent function g(z)=z+b2z2+b3z3+… such that |f′(z)g′(z)−1|<1 for |z|<1. Several theorems are proved with sharp results for the radius of convexity of the subfamilies of functions associated with the cases: g(z) is starlike for |z|<1, g(z) is convex for |z|<1, Re{g′(z)}>α(α=0,1/2).http://dx.doi.org/10.1155/S0161171280000361univalentanalyticstarlikeconvexradius of starlikeness and radius of convexiy. |
| spellingShingle | J. S. Ratti The radius of convexity of certain analytic functions II International Journal of Mathematics and Mathematical Sciences univalent analytic starlike convex radius of starlikeness and radius of convexiy. |
| title | The radius of convexity of certain analytic functions II |
| title_full | The radius of convexity of certain analytic functions II |
| title_fullStr | The radius of convexity of certain analytic functions II |
| title_full_unstemmed | The radius of convexity of certain analytic functions II |
| title_short | The radius of convexity of certain analytic functions II |
| title_sort | radius of convexity of certain analytic functions ii |
| topic | univalent analytic starlike convex radius of starlikeness and radius of convexiy. |
| url | http://dx.doi.org/10.1155/S0161171280000361 |
| work_keys_str_mv | AT jsratti theradiusofconvexityofcertainanalyticfunctionsii AT jsratti radiusofconvexityofcertainanalyticfunctionsii |