Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex of two distributions from case consecutive to general spacings. The sufficient conditions given in terms expected proportional shortfall order. As an application, compare deprivation within some parametric families income distributions.

In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and investigate some related properties. Some inequalities involving the generalized are pointed out as well.