Refinements of Cauchy-Bunyakovsky-Schwartz inequality and Bergstrom inequality with applications

Abstract

The present paper proposes some generalizations of Cauchy-Bunyakovsky-Schwarz inequality and some improvements of the Bergström inequality based on the newly obtained results. Also, improvements of the Bergström inequality based on Milne's inequality and Callebaut's inequality are presented. The newly acquired results are particularized and new applications are presented. In the last part of the paper, the current results are applied to attain improvements of the Nesbitt inequality.