Narrow Results

Ma–Minda class (of starlike functions) consists of normalized analytic functions $f$ defined on the unit disk for which the image of the function $z{f}^{\prime }(z)/f(z)$ is contained in some starlike region lying in the right-half plane. In this paper, we obtain the best possible bounds on some initial coefficients for the inverse functions of Ma–Minda starlike functions. Further, the bounds on the Fekete–Szegö functional and the second Hankel determinant are computed for such functions. In addition, some sharp radius estimates are also determined.

Sharp bounds on the moduli difference of successive inverse and logarithmic coefficients for a class of strongly Ozaki close-to-convex functions are investigated. Relevant connections of the main results presented in this paper with existing ones are also pointed out.

In this paper, we explore a subfamily of starlike functions with respect to symmetric points allied with the hyperbolic cosine function. We study Hermitian–Toeplitz determinants of third and fourth orders for the functions belonging to this subfamily. Further, we calculate estimates on the initial successive inverse coefficients as well as logarithmic coefficients and related functionals for such functions. In addition, we also determine bounds on Hankel determinants of third order and symmetric Toeplitz determinants of second and third orders.