A Note on t-Convex Functions

In this note we discuss convexity properties of functions f: I→ [−∞,∞[ defined on an interval I⊂ℝ. One of our main results is the following: If the function f: I→ [−∞,∞[ satisfies the convexity inequality for some t∈]0, 1[, then the same holds true for all rational t∈[0, 1]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.