BRIEF STUDY ON SOME PROPERTIES OF SYMMETRIC CARDIO-BAZILEVIC FUNCTIONS

Jamiu Olusegun  HAMZAT; Olalekan  Fagbemiro

Jamiu Olusegun HAMZAT Department of Mathematics, University of Lagos, Akoka, Lagos State, Nigeria.
Olalekan Fagbemiro Department of Mathematics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria.

Keywords: Analytic, Bazilevic function, Fekete-Szego, geometry, symmetric cardio-Bazilevic function

Abstract

Bazilevic functions consist of functions dened by certain integral 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 Function Theory, GFT) have had to study dierent 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. Consequently, in this article, with the aid of Salagean derivative operator, the author derived a new Bazilevic class B^α_n (A;B;α), type α, associated with symmetric cardioid domain. This was achieved via the Hadamard product of certain fractional analytic function g(z)^α 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 first three Taylor-Maclaurin coefficients 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 Mathematical approach.

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