An application of a subordination chain
Let K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ s...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203204087 |
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| author | Sukhjit Singh Sushma Gupta |
| author_facet | Sukhjit Singh Sushma Gupta |
| author_sort | Sukhjit Singh |
| collection | DOAJ |
| description | Let K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ stands for
subordination. |
| format | Article |
| id | doaj-art-a6959d0d8ed94e0e878f6ceac53dc570 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a6959d0d8ed94e0e878f6ceac53dc5702025-08-20T03:38:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003271751175410.1155/S0161171203204087An application of a subordination chainSukhjit Singh0Sushma Gupta1Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, IndiaLet K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ stands for subordination.http://dx.doi.org/10.1155/S0161171203204087 |
| spellingShingle | Sukhjit Singh Sushma Gupta An application of a subordination chain International Journal of Mathematics and Mathematical Sciences |
| title | An application of a subordination chain |
| title_full | An application of a subordination chain |
| title_fullStr | An application of a subordination chain |
| title_full_unstemmed | An application of a subordination chain |
| title_short | An application of a subordination chain |
| title_sort | application of a subordination chain |
| url | http://dx.doi.org/10.1155/S0161171203204087 |
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