Hyers-Ulam stability of Lagrange's mean value points in two variables (Q1634663)

Summary: Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange's mean value points \((\eta, \xi)\) which satisfy the equation, \(f(u, v) - f(p, q) = (u - p) f_x(\eta, \xi) +(v - q) f_y(\eta, \xi)\), where \((p, q)\) and \((u, v)\) are distinct points in the plane. Moreover, we introduce an efficient algorithm for applying our main result in practical use.