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