Displaying similar documents to “Some radius of convexity problems for certain classes of analytic functions.”

On a generalization of close-to-convex functions

Swadesh Kumar Sahoo, Navneet Lal Sharma (2015)

Annales Polonici Mathematici

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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...

Convex combination of analytic functions

Nak Eun Cho, Naveen Kumar Jain, V. Ravichandran (2017)

Open Mathematics

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Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).