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

Soon-Mo Jung and Ji-Hye Kim
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Soon-Mo Jung: Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
Ji-Hye Kim: Department of Mathematics Education, Korea National University of Education, Cheongjusi, Chungbuk 28173, Korea

Mathematics, 2018, vol. 6, issue 11, 1-8

Abstract: Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange’s mean value points ( η , ξ ) which satisfy the equation, f ( u , v ) − f ( p , q ) = ( u − p ) f x ( η , ξ ) + ( v − q ) f y ( η , ξ ) , 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.

Keywords: Hyers-Ulam stability; mean value theorem; Lagrange’s mean value point; two-dimensional Lagrange’s mean value point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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