SOME WEIGHTED INEQUALITIES for HIGHER-ORDER PARTIAL DERIVATIVES in TWO DIMENSIONS and ITS APPLICATIONS

Abstract

We establish some Ostrowski type inequalities involving higher-order partial derivatives for two dimensional integrals on Lebesgue spaces (L?, Lp and L<inf>1</inf>). Some applications in Numerical Analysis in connection with cubature formula are given. Finally, with the help of obtained inequality, we establish applications for the kth moment of random variables. © 2023 Elsevier B.V., All rights reserved.