On a functional equation. (Short Communication).
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...
We give a Hölder type estimate for normalized ρ-quasisymmetric functions, improving some results of J. Zając.
We prove a theorem on the growth of a solution of a kth-order linear differential equation. From this we obtain some uniqueness theorems. Our results improve several known results. Some examples show that the results are best possible.