Let denote the class of analytic functions in the unit disc of the form
and let denote the subclass of consisting of univalent functions. Let be an analytic function in with positive real part, , which maps onto a region starlike with respect to 1 and symmetric with respect to the real axis. Then let be the class of functions with , and let be the class of functions with , where denotes subordination between analytic functions. These classes were introduced and studied by W. Ma and D. Minda [Li, Zhong (ed.) et al., Proceedings of the conference on complex analysis, held June 19–23, 1992 at the Nankai Institute of Mathematics, Tianjin, China. Cambridge, MA: International Press. Conf. Proc. Lect. Notes Anal. 1, 157–169 (1994; Zbl 0823.30007)].
In this paper the authors consider the more general class which is defined as follows. For let be the class of functions with . For the authors prove a sharp coefficient estimate for in terms of , and the Taylor coefficients and of . As an application of the main result, they prove a respective estimate for a class of analytic functions which are defined by convolution (Hadamard product), and as a special case they obtain such an estimate for a class of functions defined by fractional derivatives.