A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli

Let S*(RL) denote the class of all analytic functions f in the open unit disk with the normalizations f(0) = f'(0) - 1 = 0 such that zf'(z)/f(z) lies in the interior of the left-half of the shifted lemniscate of Bernoulli ((x-root 2)(2) + y(2))(2) - 2((x-root 2)(2) - y(2)) = 0. In this paper, we investigate the geometric properties of functions in this class and compute the S*(RL)-radius for functions belonging to several interesting classes.