Hyers-Ulam Stability of Lagrange's Mean Value Points in Two Variables

Abstract

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.