Abstract We establish some interesting refinements of the $(p,q)$ ( p , q ) -Hölder integral inequality and -power-mean inequality. As applications, we show that existing -integral inequalities can be improved by results obtained in this paper.

Abstract Restarting a deterministic process always impedes its completion. However, it is known that restarting random can lead to an opposite outcome—expediting Hence, the effect of restart contingent on underlying statistical heterogeneity process’ completion times. To quantify this we introduce novel approach research: methodology inequality indices, which widely applied in economics and soc...