On a subclass of \(\alpha\)-convex \(\lambda\)-spiral functions
Let \(MS_\alpha^\lambda[A,B]\) be the subclass consisting of normalized analytic functions \(f(z)=z+a_2z^2+\cdots\) on the unit disk \(\Delta\) satisfying \[ (e^{i\lambda}-\alpha \cos \lambda) zf'(z)/f(z) + \alpha \cos \lambda (1+zf''(z)/f'(z)) \prec \cos\lambda ((1+Az)/(1+Bz))+i\sin\alpha, \] where \(\alpha \) and \(\lambda\) are real numbers, \(|\lambda|< \pi/2\) and \(-1\leq B < A\leq 1\). This class is a subclass of the class of \(\alpha\)-convex \(\lambda\)-spiral functions. In this paper, the authors have shown that the function in the class \(MS_\alpha^\lambda[A,B]\) are \(\lambda\)-spiral-like. An integral representation and a sharp estimate for \(|a_3-\mu a_2^2|\) and the covering theorem are obtained. The \(MS_\alpha^\beta[A,B]\) radius of functions in \(MS_\alpha^\lambda[A,B]\) is also computed.
scientific article; zbMATH DE number 1779106