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

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.

AmSTeX, 7 pages, amsppt style

References in corpus (2)

• A conjecture on some estimates for integrals
• Three equivalent conjectures on an estimate of integrals (in Russian)

Cited by in corpus (1)

• A counterexample to Khabibullin's conjecture for integral inequalities