Document Type : Research Paper

Authors

• Matina J. Rassias ¹
• P. Narasimman ²
• Choonkil Park ³
• Jung Rye Lee ⁴

¹ University College London, Department of Statistical Science, 1-19 Torrington Place, London, UK

² Department of Mathematics, Thiruvalluvar University College of Arts and Science, Kariyampatti, Tirupattur-635 901, Tamilnadu, India

³ Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

⁴ Department of Data Science, Daejin University, Kyunggi 11159, Korea

Abstract

In this article, we introduce a new generalized Euler-Lagrange $(m,n)$-cubic functional equation with its general solution. Also, we investigate its various stabilities related to the Ulam problem in fuzzy normed linear spaces using Felbin's concept. Also, we provide a counter-example for the non-existence of stability of a generalized Euler-Lagrange $(m,n)$-cubic functional equation.

Keywords

• Euler-Lagrange cubic functional equation
• Hyers-Ulam stability
• generalized Hyers-Ulam- stability
• Fuzzy normed linear space