Subfunctions and Integral Means

Authors

Gary C. Anderson, University of Nebraska-Lincoln

Date of this Version

5-1-1958

Document Type

Thesis

Citation

Thesis (M.A.)—University of Nebraska—Lincoln, 1958. Department of Mathematics.

Comments

Copyright 1958, the author. Used by permission.

Abstract

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, G_h(x) , developed in this last section, we have shown an analogy between the two situations.

Advisor: Lloyd K. Jackson