Hyers-Ulam Stability of Two-Dimensional Flett's Mean Value Points
- Authors
- Jung, Soon-Mo; Kim, Ji-Hye; Nam, Young Woo
- Issue Date
- Aug-2019
- Publisher
- MDPI
- Keywords
- Hyers-Ulam stability; mean value theorem; Flett' s mean value point; two-dimensional Flett' s mean value point
- Citation
- MATHEMATICS, v.7, no.8, pp.1 - 9
- Journal Title
- MATHEMATICS
- Volume
- 7
- Number
- 8
- Start Page
- 1
- End Page
- 9
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/1264
- DOI
- 10.3390/math7080733
- ISSN
- 2227-7390
- Abstract
- If a differentiable function f : [a,b]-> R and a point eta is an element of[a,b] satisfy f(eta)-f(a)=f '(eta)(eta-a), then the point eta 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) over cap and (s) over cap of R x R, let L be the line segment joining (r) over cap and (s) over cap. If a partially differentiable function f : RxR -> R and an intermediate point (omega) over cap is an element of L satisfy f((omega) over cap)-f((r) over cap)=<(omega)over cap>-(r) over cap ,f '(<(omega)over cap)>, then the point <(omega)over cap> 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.
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