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In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szego inequality. In this work, we aim to analyze the Fekete-Szego functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szego inequality of inverse functions to these certain analytic functions are also established in this work.

Coefficient Inequalities of Functions Associated with Petal Type Domains