Close-to-convex functions with starlike powers (fungsi hampir cembung dengan kuasa bak bintang)

Abstract

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.