Solution of a 3-D cubic functional equation and its stabilityopen access
- Authors
- Govindan, Vediyappan; Park, Choonkil; Pinelas, Sandra; Baskaran, S.
- Issue Date
- 2020
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- cubic functional equation; fuzzy normed space; Hyers-Ulam stability; fixed point method
- Citation
- AIMS MATHEMATICS, v.5, no.3, pp.1693 - 1705
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS MATHEMATICS
- Volume
- 5
- Number
- 3
- Start Page
- 1693
- End Page
- 1705
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/146505
- DOI
- 10.3934/math.2020114
- ISSN
- 2473-6988
- Abstract
- In this paper, we define and find the general solution of the following 3-D cubic functional equation
f (2x(1) + x(2) + x(3)) = 3f (x(1)+ x(2) + x(3)) + f (-x(1) + x(2) + x(3)) + 2f (x(1) + x(2)) + 2f (x(1)+ x(3)) -6f (x(1 )- x(2)) - 6f (x(1 )- x(3)) - 3f (x(2) + x(3)) + 2f (2x(1) - x(2)) + 2f (2x(1) - x(3)) - 18f (x(1)) - 6f (x(2)) - 6f (x(3))
We also prove the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by using the direct method and the fixed point method.
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