Extensions and demonstrations of Hölder’s inequality

Abstract

Abstract In this paper, we present some new extensions of Hölder’s inequality and give a condition under which the equality holds. We also show that many existing inequalities related to the Hölder inequality are particular cases of the inequalities presented. At the same time, we further promote new inequalities based on the already introduced Hölder inequality.

Keywords

• Hölder’s inequality
• Cauchy’s inequality
• Refinement
• Generalization
• Concave functions