O funkcích prostých
The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in...
Let denote the class of functions univalent and holomorphic in the unit disc . In the paper we obtain an estimate of the functional in the class for arbitrarily fixed and . Hence, for some special values of the parameters, we obtain estimates of several interesting functionals and numerous applications. A few open problems of a similar type are also formulated.
Let denote the class of functions univalent and holomorphic in the unit disc . In the paper we obtain a sharp estimate of the functional in the class for an arbitrary .