UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS
BASED ON ORDER OF CONVOLUTION CONSISTENCE
Sh. Najafzadeh$^1$, A. Ebadian$^2$, E. Amini$^3$
$^{1,2,3}$Department of Mathematics
Payme Noor University
P.O. Box 19395-4697 Tehran, IRAN
Abstract. In this paper we consider the modified Hadamard product or convolution of analytic functions with negative coefficients, combined with an Salagean integral operator. We discuss when it is a given class. Following idea of U. Bednarz and J. Sokól we shall determine the order of convolution consistence for certain analytic functions with negative coefficients.
AMS Subject Classification: 30C45, 30C50
Key Words and Phrases: Hadamard product, analytic functions with negative coefficient, order of convolution, starlike function of order $\alpha$, convex function of order $\alpha$, extreme points


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DOI: 10.12732/ijam.v28i5.10

Volume: 28
Issue: 5
Year: 2015