On ratios of certain analytic functions

Let H(z) = f(z) /g(z) and h(z) = f'(z) / g'(z) where bath f and g are in one of the classes whose members are convex, starlike relative to the origin, or typicallyreal in the open unit disk E. Sharp bounds on ∝ and gt; 0 and β and gt; 0 such that Re {H(z) } ∝ and gt; 0, Re {h (z) } β a...