Stabilities and instabilities of Euler-Lagrange cubic functional equation
Authors
G. Ganapathy
- Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
R. Sakthi
- Department of Science and Humanities, R.M.K. College of Engineering and Technology, Puduvoyal-601 206, Tamil Nadu, India.
S. Karthikeyan
- Department of Mathematics, R.M.K. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
N. Vijaya
- Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Thandalam, Chennai-602 105, Tamil Nadu, India.
M. Suresh
- Department of Mathematics, R.M.D. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
K. Venkataramanan
- Department of Mathematics, Takshashila University, Tindivanam-604 305, Tamil Nadu, India.
Abstract
This article provides the solution and Hyers-Ulam stability results of the following Euler-Lagrange cubic functional equation
\[ (a-b)\left[(a+b)^3f\left(\frac{bx+ay}{b+a}\right)+(b-a)^3f\left(\frac{bx-ay}{b-a}\right)\right] +(a+b)\left[(a+b)^3f\left(\frac{ax+by}{a+b}\right)+(a-b)^3f\left(\frac{ax-by}{a-b}\right)\right]\]
\[=ab(a^2+b^2)[f(x+y)+f(x-y)]+2\left(a^4-b^4\right)f(x), \]
\(a\ne b; a, b\ne 0\), in Banach spaces and paranormed spaces using the direct method with suitable counterexample.
Share and Cite
ISRP Style
G. Ganapathy, R. Sakthi, S. Karthikeyan, N. Vijaya, M. Suresh, K. Venkataramanan, Stabilities and instabilities of Euler-Lagrange cubic functional equation, Journal of Mathematics and Computer Science, 35 (2024), no. 1, 82--95
AMA Style
Ganapathy G., Sakthi R., Karthikeyan S., Vijaya N., Suresh M., Venkataramanan K., Stabilities and instabilities of Euler-Lagrange cubic functional equation. J Math Comput SCI-JM. (2024); 35(1):82--95
Chicago/Turabian Style
Ganapathy, G., Sakthi, R., Karthikeyan, S., Vijaya, N., Suresh, M., Venkataramanan, K.. "Stabilities and instabilities of Euler-Lagrange cubic functional equation." Journal of Mathematics and Computer Science, 35, no. 1 (2024): 82--95
Keywords
- Cubic functional equation
- Banach spaces
- paranormed spaces
- Hyers-Ulam stability
MSC
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