A note on three-parameter families and generalized convex functions
Using a three-parameter family , the authors extend the idea by \textit{E. F. Beckenbach} [Bull. Am. Math. Soc. 43, 363--371 (1937; Zbl 0016.35202)] to two-variable functions and introduce \({\mathcal F}\)-convex, \({\mathcal F}\)-midconvex and \(({\mathcal F}, M)\)-convex functions, and prove some of their properties. It is noteworthy that \({\mathcal F}\)-convex functions defined on convex sets are continuous on the interiors of these sets, and lower-semicontinuous \({\mathcal F}\)-midconvex and \(({\mathcal F}, M)\)-convex functions are also \({\mathcal F}\)-convex. Some illustrative examples are given as well.
scientific article; zbMATH DE number 5149495