与积分平均值有关的误差估计OA

In the numerical solution process of partial differential equations,integral operators are often used to discretize continuous problems,subsequently encountering error estimation issues related to integrals in numerical solutions.Using two fundamental inequalities and four classical norms,combined with integration by parts,this paper establishes error estimates between a function and its integral average.Furthermore,it characterizes the relationship and error bounds between the integral average of the product of two functions and the product of their respective integral averages.