Integral inequalities of Hilbert's type involving Fenchel-Legendre transform with applications

Abstract

New integral inequalities of Hilbert's type are introduced through Fenchel-Legendre transform. Some of these inequalities are considered as generalizations as well as improvements of some previously proved results. Applications of the extracted inequalities are presented.

Keywords

• hilbert inequality
• schwarz inequality
• fenchel-legendre transform
• integral inequalities