Starlikeness and convexity of a class of analytic functions
Let be the class of analytic functions in the unit disk that are normalized with f(0)=f′(0)−1=0 and let −1≤B<A≤1. In this paper we study the class Gλ,α={f∈:|(1−α+αzf″(z)/f′(z))/zf′(z)/f(z)−(1−α)|<λ,z∈},0≤α≤1, and give sharp sufficient conditions that embed it into the classes S∗[A,B]={f∈:zf′...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/38089 |
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| author | Nikola Tuneski Hüseyin Irmak |
| author_facet | Nikola Tuneski Hüseyin Irmak |
| author_sort | Nikola Tuneski |
| collection | DOAJ |
| description | Let be the class of analytic functions in the unit disk that
are normalized with f(0)=f′(0)−1=0 and let −1≤B<A≤1. In this paper we study the class Gλ,α={f∈:|(1−α+αzf″(z)/f′(z))/zf′(z)/f(z)−(1−α)|<λ,z∈},0≤α≤1, and give sharp sufficient conditions that embed it into the classes
S∗[A,B]={f∈:zf′(z)/f(z)≺(1+Az)/(1+Bz)}
and K(δ)={f∈:1+zf″(z)/f′(z)≺(1−δ)(1+z)/(1−z)+δ}, where “≺” denotes the usual subordination. Also, sharp upper
bound of |a2| and of the Fekete-Szegö functional |a3−μa22| is given for the class Gλ,α. |
| format | Article |
| id | doaj-art-a601e8969bb84be6a04f228cdbe032d1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a601e8969bb84be6a04f228cdbe032d12025-02-03T05:45:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/3808938089Starlikeness and convexity of a class of analytic functionsNikola Tuneski0Hüseyin Irmak1Faculty of Mechanical Engineering, Ss. Cyril and Methodius University, Karpoš II b.b., Skopje 1000, MacedoniaDepartment of Mathematics Education, Faculty of Education, Başkent University, Bağlica Campus, Bağlica, Etimesgut, Ankara 06530, TurkeyLet be the class of analytic functions in the unit disk that are normalized with f(0)=f′(0)−1=0 and let −1≤B<A≤1. In this paper we study the class Gλ,α={f∈:|(1−α+αzf″(z)/f′(z))/zf′(z)/f(z)−(1−α)|<λ,z∈},0≤α≤1, and give sharp sufficient conditions that embed it into the classes S∗[A,B]={f∈:zf′(z)/f(z)≺(1+Az)/(1+Bz)} and K(δ)={f∈:1+zf″(z)/f′(z)≺(1−δ)(1+z)/(1−z)+δ}, where “≺” denotes the usual subordination. Also, sharp upper bound of |a2| and of the Fekete-Szegö functional |a3−μa22| is given for the class Gλ,α.http://dx.doi.org/10.1155/IJMMS/2006/38089 |
| spellingShingle | Nikola Tuneski Hüseyin Irmak Starlikeness and convexity of a class of analytic functions International Journal of Mathematics and Mathematical Sciences |
| title | Starlikeness and convexity of a class of analytic functions |
| title_full | Starlikeness and convexity of a class of analytic functions |
| title_fullStr | Starlikeness and convexity of a class of analytic functions |
| title_full_unstemmed | Starlikeness and convexity of a class of analytic functions |
| title_short | Starlikeness and convexity of a class of analytic functions |
| title_sort | starlikeness and convexity of a class of analytic functions |
| url | http://dx.doi.org/10.1155/IJMMS/2006/38089 |
| work_keys_str_mv | AT nikolatuneski starlikenessandconvexityofaclassofanalyticfunctions AT huseyinirmak starlikenessandconvexityofaclassofanalyticfunctions |