Generalized Euler-Lagrange (m,n)-cubic functional equation and its stability

Rassias, Matina J.; Narasimman, P.; Park, Choonkil; Lee, Jung Rye

doi:10.22075/ijnaa.2022.28235.3840

Generalized Euler-Lagrange (m,n)-cubic functional equation and its stability

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

10.22075/ijnaa.2022.28235.3840

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