Radius of Star-Likeness for Certain Subclasses of Analytic Functions

In this paper, we investigate a normalized anal tic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition R(f(z)/g(z) ) > 0, for some analytic function, g, with R((z+1)(-2n)/z)g(z) > 0, for all n is an element of N. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp.