On a subclass of α-convex λ-spiral functions
Let H denote the class of functions f(z)=z+∑k=2∞akzk which are analytic in the unit disc Δ={z:|z|<1}. In this paper, we introduce the class Mαλ[A,B] of functions f∈H with f(z)f′(z)/z≠0, satisfying for z∈Δ:{(eiλ−αcosλ)(zf′(z)/f(z))+αcosλ(1+zf″(z)/f′(z))}≺cosλ((1+Az)/(1+Bz))+isinλ, where ≺ denotes...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011110 |
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doaj-5cfbc6d5d00b4006be30d50c5f985b0a2020-11-25T00:55:47ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130317718310.1155/S0161171202011110On a subclass of α-convex λ-spiral functionsF. M. Al-Oboudi0M. M. Hidan1Department of Mathematics, Girl's College of Education, Science Sections, Sitteen Street, Malaz, Riyadh, Saudi ArabiaDepartment of Mathematics, Girl's College of Education, Science Sections, Kabel, Abha, Saudi ArabiaLet H denote the class of functions f(z)=z+∑k=2∞akzk which are analytic in the unit disc Δ={z:|z|<1}. In this paper, we introduce the class Mαλ[A,B] of functions f∈H with f(z)f′(z)/z≠0, satisfying for z∈Δ:{(eiλ−αcosλ)(zf′(z)/f(z))+αcosλ(1+zf″(z)/f′(z))}≺cosλ((1+Az)/(1+Bz))+isinλ, where ≺ denotes subordination, α and λ are real numbers, |λ|<π/2 and −1≤B<A≤1. Functions in Mαλ[A,B] are shown to be λ-spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.http://dx.doi.org/10.1155/S0161171202011110 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
F. M. Al-Oboudi M. M. Hidan |
| spellingShingle |
F. M. Al-Oboudi M. M. Hidan On a subclass of α-convex λ-spiral functions International Journal of Mathematics and Mathematical Sciences |
| author_facet |
F. M. Al-Oboudi M. M. Hidan |
| author_sort |
F. M. Al-Oboudi |
| title |
On a subclass of α-convex λ-spiral functions |
| title_short |
On a subclass of α-convex λ-spiral functions |
| title_full |
On a subclass of α-convex λ-spiral functions |
| title_fullStr |
On a subclass of α-convex λ-spiral functions |
| title_full_unstemmed |
On a subclass of α-convex λ-spiral functions |
| title_sort |
on a subclass of α-convex λ-spiral functions |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
Let H denote the class of functions f(z)=z+∑k=2∞akzk which are analytic in the unit disc Δ={z:|z|<1}. In this paper, we introduce the class
Mαλ[A,B] of functions f∈H with f(z)f′(z)/z≠0, satisfying for z∈Δ:{(eiλ−αcosλ)(zf′(z)/f(z))+αcosλ(1+zf″(z)/f′(z))}≺cosλ((1+Az)/(1+Bz))+isinλ, where ≺ denotes subordination, α and λ are real numbers, |λ|<π/2
and
−1≤B<A≤1. Functions in
Mαλ[A,B] are shown to be λ-spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given. |
| url |
http://dx.doi.org/10.1155/S0161171202011110 |
| work_keys_str_mv |
AT fmaloboudi onasubclassofaconvexlspiralfunctions AT mmhidan onasubclassofaconvexlspiralfunctions |
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1725229458858704896 |