Document Type : Research Paper

Authors

• S. Shakeri ¹
• R. Saadati ¹
• C. Park ²

¹ Department of Mathematics, Islamic Azad University-Aiatollah Amoli Branch, Amol, P.O. Box 678, Iran

² Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea

Abstract

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation
$$f(x+y)+f(x-y)=2f(x)+2f(y)$$
in non-Archimedean $\mathcal{L}$-fuzzy normed spaces.

Keywords

• $mathcal{L}$-fuzzy metric and normed spaces
• intuitionistic fuzzy metric and normed spaces
• generalized Hyers-Ulam stability
• quadratic functional equation
• non-Archimedean $mathcal{L}$-fuzzy normed space