On the Analytical Determination of Geometric Characterizations of Analytic Functions

Year 2023, Volume: 4 Issue: 1, 9 - 15, 31.01.2023

Alaattin Akyar

https://doi.org/10.54974/fcmathsci.1094167

Abstract

As it is known, there are many sufficient conditions for the classification complex functions of one variable f(z), which are analytic and univalent in the open unit disc U = {z ∈ C ∶ SzS < 1}, and are also normalized with f(0) = 1 − f′(0) = 0 which are also known as normalization conditions. In this sense, the main goal of present article is to derive some special sufficient conditions for f(z) to be starlike of order 2−r and convex of order 2−r in U , with r is a positive integer.

Keywords

Analytic function, convex function, starlike function, univalent function

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