Some Weighted Inequalities for Higher-Order Partial Derivatives in Two Dimensions and Its Applications

Samet Erden (Bartın University)
M. Zeki Sarikaya (Duzce University)

Journal of the Indonesian Mathematical Society
VOLUME 26 NUMBER 3 (NOVEMBER 2020)

We establish some Ostrowski type inequalities involving higher-order partial derivatives for two-dimensional integrals on Lebesgue spaces (L_{∞}, L_{p} and L₁). 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.