On certain classes of close-to-convex functions

Khalida Inayat Noor

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

Abstract:

A function f , analytic in the unit disk E and given by , f ( z ) = z + ∑ k = 2 ∞ a n z k is said to be in the family K n if and only if D n f is close-to-convex, where D n f = z ( 1 − z ) n + 1 ∗ f , n ∈ N 0 = { 0 , 1 , 2 , … } and ∗ denotes the Hadamard product or convolution. The classes K n are investigated and some properties are given. It is shown that K n + 1 ⫅ K n and K n consists entirely of univalent functions. Some closure properties of integral operators defined on K n are given.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:921640

DOI: 10.1155/S0161171293000390

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