Some reverse $l_p$-type inequalities involving certain quasi monotone sequences

TL;DR

This paper establishes reverse $l_p$-type inequalities for quasi monotone sequences, extending classical inequalities like Copson's and Leindler's with reversed signs, providing new bounds for specific sequence classes.

Contribution

It introduces novel reverse $l_p$-type inequalities for quasi monotone sequences, including special cases for decreasing sequences, expanding the theoretical framework of sequence inequalities.

Findings

Reverse inequalities for non-negative decreasing sequences derived

Connections established with Copson's and Leindler's inequalities

New bounds for quasi monotone sequences presented

Abstract

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson's and Leindler's inequalities, but the sign of the inequalities is reversed.