Radius problems for a subclass of close-to-convex univalent functions
Let P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The f...
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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/S0161171292000930 |
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| author | Khalida Inayat Noor |
| author_facet | Khalida Inayat Noor |
| author_sort | Khalida Inayat Noor |
| collection | DOAJ |
| description | Let P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved. |
| format | Article |
| id | doaj-art-8230cff7196241c2bd6d47f25331a11e |
| institution | Kabale University |
| 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-8230cff7196241c2bd6d47f25331a11e2025-02-03T05:53:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115471972610.1155/S0161171292000930Radius problems for a subclass of close-to-convex univalent functionsKhalida Inayat Noor0Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaLet P[A,B], −1≤B<A≤1, be the class of functions p such that p(z) is subordinate to 1+Az1+Bz. A function f, analytic in the unit disk E is said to belong to the class Kβ*[A,B] if, and only if, there exists a function g with zg′(z)g(z)∈P[A,B] such that Re(zf′(z))′g′(z)>β, 0≤β<1 and z∈E. The functions in this class are close-to-convex and hence univalent. We study its relationship with some of the other subclasses of univalent functions. Some radius problems are also solved.http://dx.doi.org/10.1155/S0161171292000930close-to-convexstarlike univalentconvexradius of convexity. |
| spellingShingle | Khalida Inayat Noor Radius problems for a subclass of close-to-convex univalent functions International Journal of Mathematics and Mathematical Sciences close-to-convex starlike univalent convex radius of convexity. |
| title | Radius problems for a subclass of close-to-convex univalent functions |
| title_full | Radius problems for a subclass of close-to-convex univalent functions |
| title_fullStr | Radius problems for a subclass of close-to-convex univalent functions |
| title_full_unstemmed | Radius problems for a subclass of close-to-convex univalent functions |
| title_short | Radius problems for a subclass of close-to-convex univalent functions |
| title_sort | radius problems for a subclass of close to convex univalent functions |
| topic | close-to-convex starlike univalent convex radius of convexity. |
| url | http://dx.doi.org/10.1155/S0161171292000930 |
| work_keys_str_mv | AT khalidainayatnoor radiusproblemsforasubclassofclosetoconvexunivalentfunctions |