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For $0<\alpha\leq1$ and $\lambda>0,$ let \begin{equation}\label{1}  G_{\lambda,\alpha}=\left\{f\in\mathcal{A}:\left|\dfrac{1-\alpha+\alphazf''(z)/f'(z)}{zf'(z)/f(z)}-(1-\alpha)\right|<\lambda, z\in\mathbb{D}\right\},\end{equation} the general form of Silverman class introduced by Tuneski andIrnak. For this class we derive some sufficient conditions in the form ofdifferential inequalities. Further, we consider the class $\Omega,$ given by\begin{equation}\label{omega}  \Omega=\left\{f\in\mathcal{A}:|zf'(z)-f(z)|<\dfrac{1}{2},\;z\in\mathbb{D}\right\}.\end{equation} For the above two classes, we establish inclusion relationsinvolving some other well known subclasses of $\mathcal{S}^*$ and find radiusestimates for different pairs involving these classes.

Sufficient conditions and radius problems for the Silverman class