Close-to-convex functions with starlike powers (fungsi hampir cembung dengan kuasa bak bintang)
Let Kα be the set of functions f, analytic in z∈ D = {z : z < 1} satisfying ( ) ( ) Re 0 ( ) / z f z g z α ′ > , for g starlike in D and 0 ≤α ≤ 1. It is shown that such functions form a subset of the close-to-convex functions. Sharp bounds for the coefficients are gi...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2015
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| Online Access: | http://journalarticle.ukm.my/9477/ http://journalarticle.ukm.my/9477/ http://journalarticle.ukm.my/9477/1/jqma-11-1-paper2.pdf |
| Summary: | Let Kα be the set of functions f, analytic in z∈ D = {z : z < 1} satisfying
( )
( )
Re 0
( ) / z
f z
g z α
′
>
, for g starlike in D and 0 ≤α ≤ 1. It is shown that such functions form
a subset of the close-to-convex functions. Sharp bounds for the coefficients are given and the
Fekete-Szegö problem is solved.
Keywords: univalent functions; starlike functions; close-to-convex functions; coefficients;
Fekete-Szegö
ABSTRAK
Andaikan Kα set fungsi f, analisis dalam z∈ D = {z : z < 1} memenuhi
( )
( )
0
( ) / z
f z
Ny
g z α
′
>
, untuk g bak bintang dalam D dan 0 ≤α ≤ 1. Dapat ditunjukkan bahawa
fungsi tersebut merupakan subset bagi suatu set fungsi hampir cembung. Batas-batas terbaik
bagi pekali diberikan dan masalah Fekete-Szegö diselesaikan. |
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