Sharp coefficient estimates for certain subclasses of univalent functions associated with Nephroid domain

Abstract

In this article, first of all we introduce a newly defined class of analytic functions associated
with Nephroid shaped domain and explores their coefficient properties. We determine sharp bounds for
the initial coefficients including a sharp Fekete-Szeg¨o inequality. The study also investigates exact bounds
for Hankel determinants of different order. We derive bounds for the inverse coefficients and logarithmic
coefficients, and also sharpness of some of these estimates. Finally, this article demonstrates the sharpness
of the Zalcman functional and the Krushkal inequality as a particular cases. Additionally, we examines how
coefficient estimation, growth and distortion theorems reveal the relationship between an analytic functions
structure and its behavior for different class by using the concept of carath`eodory functions.