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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
##### Keywords:
two-dimensional Lagrange’s mean value point
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##### References:
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