International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 319-328
doi:10.1155/S0161171293000389
On certain classes of p-valent analytic functions
Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737, Korea
Received 5 November 1991
Copyright © 1993 Nak Eun Cho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 Jp,c(f), defined by
Jp,c(f)=c+pzc∫0ztc−1f(t)dt (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 Tp(α,β) of analytic functions with negative coefficients.