Logarithmic coefficients for exponential classes of starlike and convex functions

Abstract

In this paper, we investigate two subclasses of univalent functions associated with the exponential mapping $\phi (z)=e^{\alpha z},0<\alpha \le 1,$ defined via the subordination conditions $\frac{z{f}^{\prime }(z)}{f(z)}\prec e^{\alpha z}\text{and}1+\frac{z{f}^{\prime \prime }(z)}{f^{\prime }(z)}\prec e^{\alpha z}.$ These classes provide a natural exponential analogue of several classical subclasses arising in geometric function theory. We obtain sharp coefficient estimates, logarithmic coefficient inequalities and sharp bounds for the associated Hankel determinants. In particular, explicit estimates are derived for $H_{2,1}(F_f/2)$ for functions belonging to the exponential subclasses introduced above of starlike and convex functions. Our results extend and unify several earlier works on exponential subclasses and highlight connections with logarithmic coefficients and determinant functionals.