On a class of p -valent close-to-convex functions of order β and type α

M. K. Aouf

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

Let S ( A , B , p , α ) denote the class of functions g ( z ) = z p + ∑ n = p + 1 ∞ b n z n analytic in the unit disc U = { z : | z | < 1 } and satisfying the condition z g ′ ( z ) g ( z ) < p + [ p B + ( A − B ) ( p − α ) ] z 1 + B z , z ∈ U , − 1 ≦ B < A ≦ 1 , 0 ≦ α < p . Let C ( A , B , p , β , α ) denote the class of functions f ( z ) = z p + ∑ n = p + 1 ∞ a n z n analytic in U , and satisfying the condition Re { z f ′ ( z ) g ( z ) } > β , z ∈ U , g ∈ S ( A , B , p , α ) . In this paper we determine the coefficient estimates and distortion theorems for the class C ( A , B , p , β , α ) .

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:294247

DOI: 10.1155/S0161171288000316

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