Sufficiency for Gaussian hypergeometric functions to be uniformly convex
Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditio...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171299227652 |
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| _version_ | 1850218227856048128 |
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| author | Yong Chan Kim S. Ponnusamy |
| author_facet | Yong Chan Kim S. Ponnusamy |
| author_sort | Yong Chan Kim |
| collection | DOAJ |
| description | Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions
ℱ1 and ℱ2 and obtain conditions on the parameters a,b,c such that f∈ℱ1 implies Ia,b;c(f)∈ℱ2. |
| format | Article |
| id | doaj-art-3da8fdbafb344e8ca74b3cc4e37766d4 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3da8fdbafb344e8ca74b3cc4e37766d42025-08-20T02:07:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122476577310.1155/S0161171299227652Sufficiency for Gaussian hypergeometric functions to be uniformly convexYong Chan Kim0S. Ponnusamy1Department of Mathematics, Yeungnam University, 214-1, Daedong, Gyongsan 712-749, KoreaDepartment of Mathematics, University of Helsinki, P. O. Box 4, Hallitskatu 15, Helsinki FIN-00014, FinlandLet F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk 𝒰. Let an operator Ia,b;c(f) be defined by [Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functions ℱ1 and ℱ2 and obtain conditions on the parameters a,b,c such that f∈ℱ1 implies Ia,b;c(f)∈ℱ2.http://dx.doi.org/10.1155/S0161171299227652 |
| spellingShingle | Yong Chan Kim S. Ponnusamy Sufficiency for Gaussian hypergeometric functions to be uniformly convex International Journal of Mathematics and Mathematical Sciences |
| title | Sufficiency for Gaussian hypergeometric functions to be uniformly convex |
| title_full | Sufficiency for Gaussian hypergeometric functions to be uniformly convex |
| title_fullStr | Sufficiency for Gaussian hypergeometric functions to be uniformly convex |
| title_full_unstemmed | Sufficiency for Gaussian hypergeometric functions to be uniformly convex |
| title_short | Sufficiency for Gaussian hypergeometric functions to be uniformly convex |
| title_sort | sufficiency for gaussian hypergeometric functions to be uniformly convex |
| url | http://dx.doi.org/10.1155/S0161171299227652 |
| work_keys_str_mv | AT yongchankim sufficiencyforgaussianhypergeometricfunctionstobeuniformlyconvex AT sponnusamy sufficiencyforgaussianhypergeometricfunctionstobeuniformlyconvex |