On certain classes of p -valent analytic functions

Nak Eun Cho

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-10

Abstract:

The objective of the present paper is to introduce a certain general class P ( p , α , β ) ( p ∈ N = { 1 , 2 , 3 , … } , 0 ≤ α < p and β ≥ 0 ) of p -valent analytic functions in the open unit disk U and we prove that if f ∈ P ( p , α , β ) then J p , c ( f ) , defined by J p , c ( f ) = c + p z c ∫ 0 z t c − 1 f ( t ) d t ( c ∈ N ) belongs to P ( p , α , β ) . We also investigate inclusion properties of the class P ( p , α , β ) . Furthermore, we examine some properties for a class T p ( α , β ) of analytic functions with negative coefficients.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:896158

DOI: 10.1155/S0161171293000389

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