$${\mathcal {S}}^{*}(\phi )$$ and $${\mathcal {C}}(\phi )$$-Radii for Some Special Functions

The radius problem explaining the geometric properties of normalized forms special functions has been interest among Geometric function theories. In this paper, we consider Ma-Minda classes analytic $${\mathcal {S}}^{*}(\phi ):= \{f\in {\mathcal {A}} : ({zf'(z)}/{f(z)}) \prec \phi (z) \}$$ and {C}}(\phi (1+{zf''(z)}/{f'(z)}) defined on unit disk $${\mathbb {D}}$$ show that {S}}^{*}(1+\alpha z)$$ {C}}(1+\alpha , $$0<\alpha \le 1$$ solve finding sharp )$$ -radii for some functions, whenever $$\phi (-1)=1-\alpha $$ . Radius strongly starlikeness is also considered.