On a class of p-valent close-to-convex functions of order and type .
Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions , a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.
MSC 2010: 30C45, 30A20, 34C40In this paper we determine conditions an analytic function g needs to satisfy in order that the function Fgiven by (1) be convex.
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...