COEFFICIENTS PROBLEMS FOR FAMILIES OF HOLOMORPHIC FUNCTIONS RELATED TO HYPERBOLA

We consider a family of analytic and normalized functions that are related to the domains H(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation 1/rho = (2 cos phi/s)(s) (0 < s <= 1, vertical bar phi vertical bar < (pi s)/2). We mainly study a coefficient problem of the families of functions for which zf'/f or 1 + zf ''/f' map the unit disk onto a subset of H(s). We find coefficients bounds, solve Fekete-Szego problem and estimate the Hankel determinant. (C) 2020 Mathematical Institute Slovak Academy of Sciences