On certain generalizations of S * ( ψ ) ${\mathcal{S}}^{\ast }(\psi )$ -II

Abstract For the Ma-Minda classes S * ( ψ ) ${\mathcal{S}}^{\ast }(\psi )$ and C ( ψ ) $\mathcal{C}(\psi )$ of starlike and convex analytic functions or their natural generalization, we establish new certain sufficient conditions and derive the sharp radius constants with respect to convolution. We also find the Bohr radius for the class S f ( ψ ) : = g ( z ) = ∑ k = 1 ∞ b k z k : g ≺ f ${S}_{f}(\psi ):=\left\{g(z)={\sum }_{k=1}^{\infty }{b}_{k}{z}^{k}:g\prec f\right\}$ of subordinants, where f ∈ S * ( ψ ) $f\in {\mathcal{S}}^{\ast }(\psi )$ . The result improves or generalizes the several well-known results.