$\alpha$-accessible domains, a nonsmooth case

This paper continues the study of $\alpha$-accessible domains in $\mathbb R^n$. They are starlike domains and satisfy cone condition which is important for applications. Conditions of $\alpha$-accessibility of domain, defined by the inequality $F(x)<0$, is obtained for a continuous function $F$ in $\mathbb R^n$. Thus these conditions are written in the form of inequalities for the directional derivatives; necessary and sufficient conditions differ only in the sign of equality in these inequalities. We obtain new results even in the case where $\alpha=0$ (the case of starlike domains).