A novel subclass of starlike functions

In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new subclass $\mathcal{S}^*(\phi)$ by considering a specific function in place of $\phi$, which is the solution of a differential subordination obtained by reformulating a differential inequality. We also study the class defined by means of a differential inequality and establish the relation between this class and $\mathcal{S}^*(\phi)$. We obtain certain inclusion and radius results for both the classes. Further, we estimate logarithmic coefficients, inverse coefficients and Fekete-Szeg\"o functional bounds for functions in $ \mathcal{S}^*(\phi)$.