Starlike functions associated with an Epicycloid

For a natural number $n\geq 2$, the function $\phi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps open unit disk onto domain bounded by an epicycloid with $(n-1)$ cusps. A class of starlike functions associated $\phi_{n\mathcal{L}}$ is defined in and its sharp bounds on initial coefficients, various inclusion relations radii problems related to other subclasses are investigated. As application, corresponding results determined limiting case for normalized analytic $f$ satisfying $|zf'(z)/f(z)-1|<1$ disk.