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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Wiley
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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| author | F. M. Al-Oboudi M. M. Hidan |
| author_facet | F. M. Al-Oboudi M. M. Hidan |
| author_sort | F. M. Al-Oboudi |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-5cfbc6d5d00b4006be30d50c5f985b0a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5cfbc6d5d00b4006be30d50c5f985b0a2025-02-03T01:10:48ZengWileyInternational 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 |
| spellingShingle | F. M. Al-Oboudi M. M. Hidan On a subclass of α-convex λ-spiral functions International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | On a subclass of α-convex λ-spiral functions |
| title_sort | on a subclass of α convex λ spiral functions |
| url | http://dx.doi.org/10.1155/S0161171202011110 |
| work_keys_str_mv | AT fmaloboudi onasubclassofaconvexlspiralfunctions AT mmhidan onasubclassofaconvexlspiralfunctions |