Let denote the class of functions , regular and normalized in the unit disk . The author studies the relation between two subclasses of , the class of starlike functions of order , ,
and the class of uniformly starlike functions
F. Rønnig [J. Math. Anal. Appl. 194, No. 1, 319-327 (1995; Zbl 0834.30011)] showed that and posed the problem of determining the largest such that . The author proved that if , then . The bound is determined as , where is the maximum of the function
in the square which is attained for , .