Coefficient inequalities for analytic functions associated with cardioid domains

Abstract

The geometry of image domain of analytic functions is of substantial importance to have a comprehensive study of analytic functions. Malik et al. [Analytic functions associated with cardioid domain, submitted] introduced a new class of functions connected with cardioid domain and established coefficient bounds for functions in this class. Also the bounds for the coefficients of Taylor series and their related functional inequalities are of major interest. In this article, we aim to find the sharp bounds for the coefficients and to estimate the Fekete-Szegö functional for certain analytic functions associated with cardioid domain. The same type results are obtained for inverse functions and for $\log(f(z)/z)$.