On radii of convexity and starlikeness of some classes of analytic 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. Let P(α1) be the class of functions with positive real part greater than α1, 0≤α1≤1. It is clear that p[A,B]⊂P(1−A1−B)⊂P[1,−1]. The principal results in this paper are the determination of the radius of...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129100100X |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849683550398316544 |
|---|---|
| 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. Let P(α1) be the class of functions with positive real part greater than α1, 0≤α1≤1. It is clear that
p[A,B]⊂P(1−A1−B)⊂P[1,−1]. The principal results in this paper are the determination of the radius of
β-starlikeness and β-convexity of f(z) with β=1−A1−B, when f(z) is restricted to certain classes of univalent
and analytic functions related vith P[A,B]. |
| format | Article |
| id | doaj-art-d4a6afffe15d4ec9ac556d221bf317e1 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d4a6afffe15d4ec9ac556d221bf317e12025-08-20T03:23:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114474174610.1155/S016117129100100XOn radii of convexity and starlikeness of some classes of analytic 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. Let P(α1) be the class of functions with positive real part greater than α1, 0≤α1≤1. It is clear that p[A,B]⊂P(1−A1−B)⊂P[1,−1]. The principal results in this paper are the determination of the radius of β-starlikeness and β-convexity of f(z) with β=1−A1−B, when f(z) is restricted to certain classes of univalent and analytic functions related vith P[A,B].http://dx.doi.org/10.1155/S016117129100100Xsubordinatestarlike and convex functionsbounded boundary rotation radiusclose-to-convex functions. |
| spellingShingle | Khalida Inayat Noor On radii of convexity and starlikeness of some classes of analytic functions International Journal of Mathematics and Mathematical Sciences subordinate starlike and convex functions bounded boundary rotation radius close-to-convex functions. |
| title | On radii of convexity and starlikeness of some classes of analytic functions |
| title_full | On radii of convexity and starlikeness of some classes of analytic functions |
| title_fullStr | On radii of convexity and starlikeness of some classes of analytic functions |
| title_full_unstemmed | On radii of convexity and starlikeness of some classes of analytic functions |
| title_short | On radii of convexity and starlikeness of some classes of analytic functions |
| title_sort | on radii of convexity and starlikeness of some classes of analytic functions |
| topic | subordinate starlike and convex functions bounded boundary rotation radius close-to-convex functions. |
| url | http://dx.doi.org/10.1155/S016117129100100X |
| work_keys_str_mv | AT khalidainayatnoor onradiiofconvexityandstarlikenessofsomeclassesofanalyticfunctions |