Refined and Generalized Versions of Hölder’s Inequality via Schur Convexity of Functions

In this paper, we introduce a class of functions associated with Hölder’s inequality and show the Schur convexities of these functions. With the help of Schur convexity, several improved versions of Hölder’s inequality are established. The results obtained here are the generalizations and refinements of the existing results for Hölder’s inequality. At the end of the paper, we provide an application of the present result to the improvement of Minkowski’s inequality.