Vol.:(0123456789)
The Journal of Analysis
https://doi.org/10.1007/s41478-019-00178-0
1 3
ORIGINAL RESEARCH PAPER
An n‑dimensional cubic functional equation and its
Hyers–Ulam stability
Abasalt Bodaghi
1
· Sandra Pinelas
2
· Govindan Vediyappan
3
·
Kokila Gunesekaran
4
Received: 8 January 2019 / Accepted: 7 May 2019
© Forum D’Analystes, Chennai 2019
Abstract
In this article, we introduce and discuss the general solution of a new n-dimensional
cubic functional equation. Furthermore, we establish the generalized Hyers–Ulam
stability of this functional equation in fuzzy normed spaces using direct and fixed
point approach.
Keywords Cubic functional equation · Fixed point · Hyers–Ulam stability · Fuzzy
normed space
Mathematics Subject Classification 39B52 · 39B72 · 39B82
* Abasalt Bodaghi
abasalt.bodaghi@gmail.com
Sandra Pinelas
sandra.pinelas@gmail.com
Govindan Vediyappan
govindoviya@gmail.com
Kokila Gunesekaran
kokilabalachandar@gmail.com
1
Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
2
Departmento de Cie Ncias Exatas e Engenharia, Academia Militar, Lisbon, Portugal
3
Department of Mathematics, Sri Vidya Mandir Arts and Science College, Uthangarai,
Tamil Nadu 636 902, India
4
Department of Mathematics, Government Arts and Science College (Men), Krishnagiri,
Tamil Nadu 635 001, India