Close-to-convex functions associated with a cubic polynomial $1+z-(z^3/3)$

Abstract

In this paper, we introduce a subclass of close-to-convex functions associated with  a cubic polynomial  $1+z-(z^3/3)$ which is the Carath\'{e}odary function and related to the nephroid shaped bounded domain. We discuss the growth and distortion theorems and certain coefficient inequalities using the concept of subordination for such functions. We also determine bounds on initial inverse coefficients, logarithmic coefficients and logarithmic coefficients for the inverse function. Moreover, we compute bounds of  the second order Hankel determinants and Schwarzian derivatives.