New refinements of generalized Hölder’s inequality and their applications. (English) Zbl 1351.26045
Summary: In this paper, we present a series of sharpened versions of generalized Hölder’s inequality. As an application in information theory, we give a new refinement of Singh’s inequality with respect to the ‘useful’ information of order \(\alpha\) for the power distribution. The Singh’s inequality include Shannon’s inequality as a special case.