New property of a generalized Hölder’s inequality and its applications

In this paper, we present a new property of a generalized Hölder’s inequality, and then we obtain a new refinement of the generalized Hölder’s inequality. As applications, we give a generalization and refinement of the Opial–Beesack inequality by using the obtained result. Moreover, as an application in information theory, we give a refinement of Singh’s inequality which is a generalized Shannon’s inequality.