BRIEF STUDY ON SOME PROPERTIES OF SYMMETRIC CARDIO-BAZILEVIC FUNCTIONS

Abstract

Bazilevic functions consist of functions de ned by certain integral

I say, which are entirely univalent in the unit disk. They contain some other

class of functions as special cases. In the recent time, the study of Bazilevic

functions became so popular that researchers (especially in Geometric Func-

tion Theory, GFT) have had to study di erent subclasses of Bazilevic functions

as related to various domains. However, their study seem to lack full vigour

addressing relevant connections of Bazilevic functions to certain interesting

domain called the symmetric cardioid domain. In characterization of these

Bazilevic functions, the geometry of the image domains is very critical. Conse-

quently, in this article, with the aid of Salagean derivative operator, the author

derived a new Bazilevic class B 

n (A;B;  ), type  , associated with symmetric

cardioid domain. This was achieved via the Hadamard product of certain frac-

tional analytic function g(z)  and the normalized univalent function f(z) using

subordination principle. In the sequel, a new geometrical formation regarding

the said class of Bazilevic functions was obtained. Additionally, sharp bounds

on the  rst three Taylor-Maclaurin coe cients for functions belonging to the

aforementioned class were obtained while the relationship of these bounds to

the classical Fekete-Szego inequality was established using a very lucid Math-

ematical approach.