New subclasses concerning some analytic and univalent functions (Q1653298)

Summary: Considering a function \(f(z) = z/ \left(1 - z^2\right)\) which is analytic and starlike in the open unit disc \(U\) and a function \(f(z) = z/ \left(1 - z\right)\) which is analytic and convex in \(U\), we introduce two new classes \(\mathcal{S}_\alpha^\ast(\beta)\) and \(\mathcal{K}_\alpha(\beta)\) concerning \(f_\alpha(z) = z / \left(1 - z^\alpha\right)(\alpha > 0)\). The object of the present paper is to discuss some interesting properties for functions in the classes \(\mathcal{S}_\alpha^\ast(\beta)\) and \(\mathcal{K}_\alpha(\beta)\).