Equivalent Conditions of the Reverse Hardy-Type Integral Inequalities

Abstract

Hardy-type integral inequalities play a prominent role in the study of analytic inequalities, which are essential in mathematical analysis and its various applications, such as in the study of symmetry and asymmetry phenomena. In this paper, employing methods of real analysis and using weight functions, we investigate some equivalent conditions of two kinds of reverse Hardy-type integral inequalities with a particular non-homogeneous kernel. A few equivalent conditions of two kinds of reverse Hardy-type integral inequalities with a particular homogeneous kernel are deduced in the form of applications.

Keywords

• hardy-type integral inequality
• weight function
• equivalent form
• reverse
• gamma function