Hyers-ulam stability of an n-variable quartic functional equation
- Authors
- Govindan, V.; Hwang, I.; Park, C.
- Issue Date
- 2020
- Publisher
- American Institute of Mathematical Sciences
- Keywords
- quartic functional equation; fixed point method; Hyers-Ulam stability; random normed space; direct method
- Citation
- AIMS Mathematics, v.6, no.2, pp.1452 - 1469
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS Mathematics
- Volume
- 6
- Number
- 2
- Start Page
- 1452
- End Page
- 1469
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/146495
- DOI
- 10.3934/math.2021089
- ISSN
- 2473-6988
- Abstract
- In this note we investigate the general solution for the quartic functional equation of the form
(3n + 4) f(Sigma(n)(i=1) x(i)) + Sigma(n)(j=1)f(-nx(j) + Sigma(n)(i=1,i not equal j) x(i)) = (n(2) + 2n + 1) Sigma(n)(i=1,i not equal j not equal k) f(x(i) + x(j) + x(k))
-1/2(3n(3) - 2n(2) - 13n - 8) Sigma(n)(i=1,i not equal j) f(x(i) + x(j))
+1/2(n(3) + 2n(2) + n) Sigma(n)(i=1,i not equal j) f(x(i) - x(j))
+ 1/2(3n(4) - 5n(3) - 7n(2) +13n + 12) Sigma(n)(i=1) f(x(i))
(n epsilon N, n > 4) and also investigate the Hyers-Ulam stability of the quartic functional equation in random normed spaces using the direct approach and the fixed point approach.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/146495)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.