THE RADII OF STARLIKENESS AND CONYEXITY OF ORDER ALPHA OF TYPICALLY REAL FUNCTIOI{S

Let TR denote the class of typically real functions (r) f(z): j tå;+z au<,t in the unit disc lzl = 1, where p(l) is a probability measure on [- 1, l]. Kirwan [1] has found that the radius of starlikeness of the class 7R is the number [2-1, i.e. for each function f(TR the inequality * " 'f=,(? =- oJGI holds in the disc lrl=E-l, with equality only for the functio