Coefficient bounds and convolution properties for certain classes of close-to-convex functions
In this paper, the authors introduce and study the class \(C(\varphi,\xi)\) of normalized close-to-convex functions which is defined by using the subordination for analytic functions \(\varphi\) and \(\xi\) on the unit disc. The authors derive the bounds of the quantity \(a_3-\mu a^2_2\) for the function \(f(z)=z+a_2 z^2+a_3z^3+ \dots\) in \(C(\varphi,\xi)\) in terms of \(\varphi\) and \(\xi\), where \(\mu\) is a real constant. They have shown that the class \(C(\varphi,\xi)\) is closed under the convolution operation by convex functions, or starlike functions of order 1/2 when \(\varphi\) and \(\xi\) satisfy some mild conditions.
scientific article; zbMATH DE number 1538533