New refinements of generalized Hölder's inequality and their applications

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 α for the power distribution. The Singh’s inequality include Shannon’s inequality as a special case. Mathematics subject classification (2010): 26D15, 94A17.