New subclass of analytic functions defined by subordination

By using the subordination relation "≺", we introduce an interesting subclass of analytic functions as follows: S∗α:={f∈A:zf′(z)f(z)≺1(1−z)α, |z|<1}, where 0<α≤1 and A denotes the class of analytic and normalized functions in the unit disk |z|<1. In the present paper, by the class S∗α and by the Nunokawa lemma we generalize a famous result connected to starlike functions of order 1/2. Also, coefficients inequality and logarithmic coefficients inequality for functions of the class S∗α are obtained.