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

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 ...

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 ...