In this talk we consider two classes of functional inequalities and the related functional equation. Under natural but general circumstances we show that if the solution set of the functional equation forms a 2-dimensional Beckenbach family then the continuous solutions of the functional inequality are exactly those functions which are convex with respect to the Beckenbach family. Several concrete examples and applications will be provided.
Solution methods for two variable functional inequalities
2020. 02. 27. 10:15