Non-stabilities of mixed type Euler-Lagrange k-cubic-quartic functional equation in various normed spaces

Rassias, John Michael; Arunkumar, Mohan; Sathya, Elumalai

doi:10.30495/maca.2019.679849

Non-stabilities of mixed type Euler-Lagrange k-cubic-quartic functional equation in various normed spaces

https://doi.org/10.30495/maca.2019.679849

Volume 1, Issue 1 - Serial Number 1

Journal of Mathematical Analysis and its Contemporary Applications

Winter 2019

Pages 1-43

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

John Michael Rassias ¹

Mohan Arunkumar ²

Elumalai Sathya ³

¹ Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str. Aghia Paraskevi, Athens 15342, Greece.

² Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.

³ Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai - 606 603, TamilNadu, India.

Abstract

In this paper, we introduce and examine the generalized Ulam-Hyers stability of fixed Euler-Lagrange k-Cubic-Quartic functional Equation
f(x+ky) + f(kx+y) + f(x-ky) + f(y-kx) = k²[2f(x+y) + f(x-y) + f(y-x)] + 2(k⁴-1) [f(x) + f(y)] +k²/4(k²-1) [f(2x) + f(2y)]
where k is a real number with k ≠ 0, ±1 in various Banach spaces with the help of two different methods.