A real valued function f defined on a real interval I is called (ε,δ)-convex if it satisfies f (tx+ (1-t)y)≤ tf (x)+ (1-t)f (y)+ε t (1-t)|x-y|+δ for x,y∈ I,t∈ [0,1]. The main results of the paper ...

Matrix inequalities and convex functions constitute a central theme in modern mathematical analysis, with far‐reaching implications across numerical analysis, optimisation, quantum information ...

The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of ...

Mathematically, a convex function is one for which the line connecting any two points on the graph of the function lies on or above the graph (see Figure 1). For example, suppose that a trader can ...