Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 30 September 2018 / Approved: 30 September 2018 / Online: 30 September 2018 (10:42:59 CEST)

A peer-reviewed article of this Preprint also exists.

Jung, S.-M.; Kim, J.-H. Hyers-Ulam Stability of Lagrange’s Mean Value Points in Two Variables. Mathematics 2018, 6, 216. Jung, S.-M.; Kim, J.-H. Hyers-Ulam Stability of Lagrange’s Mean Value Points in Two Variables. Mathematics 2018, 6, 216.

Journal reference: Mathematics 2018, 6, 216
DOI: 10.3390/math6110216

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.

Subject Areas

Hyers-Ulam stability; mean value theorem; Lagrange's mean value point; two-dimensional Lagrange's mean value point

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