Hyers–Ulam Stability of Two-Dimensional Flett’s Mean Value Points

Soon-Mo Jung, Ji-Hye Kim and Young Woo Nam
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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 28173, Korea
Young Woo Nam: Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea

Mathematics, 2019, vol. 7, issue 8, 1-9

Abstract: If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) − f ( a ) = f ′ ( η ) ( η − a ) , then the point η is called a Flett’s mean value point of f in [ a , b ] . The concept of Flett’s mean value points can be generalized to the 2-dimensional Flett’s mean value points as follows: For the different points r ^ and s ^ of R × R , let L be the line segment joining r ^ and s ^ . If a partially differentiable function f : R × R → R and an intermediate point ω ^ ∈ L satisfy f ( ω ^ ) − f ( r ^ ) = ω ^ − r ^ , f ′ ( ω ^ ) , then the point ω ^ is called a 2-dimensional Flett’s mean value point of f in L . In this paper, we will prove the Hyers–Ulam stability of 2-dimensional Flett’s mean value points.

Keywords: Hyers-Ulam stability; mean value theorem; Flett’s mean value point; two-dimensional Flett’s mean value point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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