Date of this Version
Thesis (M.A.)—University of Nebraska—Lincoln, 1958. Department of Mathematics.
We will develop a close analogy between convex functions and subfunctions with respect to solutions of one of the simplest second order ordinary linear differential equations. We shall introduce the concept of integral means, first with respect to convex functions and subsequently in connection with solutions of a particular differential equation. In proceeding from convex or sub-linear functions and ordinary integral means to subfunctions with respect to solutions of y” + a1y’ + a2y = 0 , a2 ≤ , and the integral mean, Gh(x) , developed in this last section, we have shown an analogy between the two situations.
Advisor: Lloyd K. Jackson