A class of univalent functions with varying arguments
f(z)=z+∑m=2∞amzm is said to be in V(θn) if the analytic and univalent function f in the unit disc E is nozmalised by f(0)=0, f′(0)=1 and arg an=θn for all n. If further there exists a real number β such that θn+(n−1)β≡π(mod2π) then f is said to be in V(θn,β). The union of V(θn,β) taken over all poss...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129200067X |
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| author | K. S. Padmanabhan M. Jayamala |
| author_facet | K. S. Padmanabhan M. Jayamala |
| author_sort | K. S. Padmanabhan |
| collection | DOAJ |
| description | f(z)=z+∑m=2∞amzm is said to be in V(θn) if the analytic and univalent function f in the unit disc E is nozmalised by f(0)=0, f′(0)=1 and arg an=θn for all n. If further there exists a real number β such that θn+(n−1)β≡π(mod2π) then f is said to be in V(θn,β). The union of V(θn,β) taken over all possible sequence {θn} and all possible real number β is denoted by V. Vn(A,B) consists of functions f∈V such thatDn+1f(z)Dnf(z)=1+Aw(z)1+Bw(z),−1≤A<B≤1, where n∈NU{0} and w(z) is analytic, w(0)=0 and |w(z)|<1, z∈E. In this paper we find the coefficient inequalities, and prove distortion theorems. |
| format | Article |
| id | doaj-art-ab4955f8d2f142f0b69fdca35237e359 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ab4955f8d2f142f0b69fdca35237e3592025-08-20T02:20:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115351752210.1155/S016117129200067XA class of univalent functions with varying argumentsK. S. Padmanabhan0M. Jayamala1The Ramanujan Institute, University of Madras, Madras 600 005, IndiaThe Ramanujan Institute, University of Madras, Madras 600 005, Indiaf(z)=z+∑m=2∞amzm is said to be in V(θn) if the analytic and univalent function f in the unit disc E is nozmalised by f(0)=0, f′(0)=1 and arg an=θn for all n. If further there exists a real number β such that θn+(n−1)β≡π(mod2π) then f is said to be in V(θn,β). The union of V(θn,β) taken over all possible sequence {θn} and all possible real number β is denoted by V. Vn(A,B) consists of functions f∈V such thatDn+1f(z)Dnf(z)=1+Aw(z)1+Bw(z),−1≤A<B≤1, where n∈NU{0} and w(z) is analytic, w(0)=0 and |w(z)|<1, z∈E. In this paper we find the coefficient inequalities, and prove distortion theorems.http://dx.doi.org/10.1155/S016117129200067Xvarying argumentsRuscheweyh derivativedistortion theoremscoefficient estimates. |
| spellingShingle | K. S. Padmanabhan M. Jayamala A class of univalent functions with varying arguments International Journal of Mathematics and Mathematical Sciences varying arguments Ruscheweyh derivative distortion theorems coefficient estimates. |
| title | A class of univalent functions with varying arguments |
| title_full | A class of univalent functions with varying arguments |
| title_fullStr | A class of univalent functions with varying arguments |
| title_full_unstemmed | A class of univalent functions with varying arguments |
| title_short | A class of univalent functions with varying arguments |
| title_sort | class of univalent functions with varying arguments |
| topic | varying arguments Ruscheweyh derivative distortion theorems coefficient estimates. |
| url | http://dx.doi.org/10.1155/S016117129200067X |
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