The radius of \(n\)-valent convexity and starlikeness for some special classes of analytical functions on a disk (Q1277445)

Let \(\tau^n_{\alpha,\theta}\) denote the class of analytic functions \(g(z)={1\over n}z^n+\cdots\) of the unit disk satisfying \(\text{Re}{1-2z^n\cos \theta+z^{2n} \over z^{n-1}}g'(z)>\alpha\). For \(n=1\) these functions are close-to-convex, hence univalent; for \(n>1\) the functions are \(n\)-valently close-to-convex. The authors compute the radius of \(n\)-valent convexity for \(\tau^n_{\alpha,\theta}\).