Some Refinements of the Improved Young and Its Reverse Inequalities

Abstract

The theory of inequality in mathematics is an extensive and interesting area of research. The classical Young inequality has a great importance in several fields of mathematics, statistics and other disciplines. Many results were obtained on refinements, generalizations and converses of the Young inequality. In this note, we mainly investigate the improved Young and its reverse inequalities. First, we present a new version of a generalization of reverse Young inequality. In addition, we also get the Young and its reverse inequalities for scalars with the classical Kantorovich constant. Finally, we establish the Young and its reverse inequalities for operators on infinite and finite dimensional Hilbert spaces.