Direct and inverse conversion formulas associated with Khabibullin's conjecture for integral inequalities

TL;DR

This paper derives inverse conversion formulas related to Khabibullin's conjecture, which involves integral inequalities for non-negative functions, providing tools for transforming between functions $q(t)$ and $g(t)$.

Contribution

The paper introduces an explicit inverse conversion formula for the integral inequalities associated with Khabibullin's conjecture, complementing the existing direct formula.

Findings

Derived an inverse conversion formula for the integral inequalities

Established a method to express $q(t)$ in terms of $g(t)$

Enhanced understanding of the relationship between $q(t)$ and $g(t)$ in Khabibullin's conjecture

Abstract

Khabibullin's conjecture deals with two linear integral inequalities for some non-negative continuous function $q(t)$. The integral in the first of these two inequalities converts $q(t)$ into another function of one variable $g(t)$. This integral yields the direct conversion formula. An inverse conversion formula means a formula expressing $q(t)$ back through $g(t)$. Such an inverse conversion formula is derived.