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Hyers-Ulam stability of Lagrange’s mean value points in two variables. (English) Zbl 1404.39031
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.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B22 Functional equations for real functions
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