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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 2, Pages 319-328
http://dx.doi.org/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 Hindawi Publishing Corporation. 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)(pN={1,2,3,}, 0α<p  and  β0) of p-valent analytic functions in the open unit disk U and we prove that if fP(p,α,β) then Jp,c(f), defined by Jp,c(f)=c+pzc0ztc1f(t)dt    (cN) 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.