Stabilities and instabilities of additive-quadratic 3D functional equations in paranormed spaces
Authors
S. Karthikeyan
- Department of Mathematics, R.M.K. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
T. R. K. Kumar
- Department of Mathematics, R.M.K. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
S. Vijayakumar
- Department of Mathematics, R.M.K. Engineering College, Kavaraipettai-601 206, Tamil Nadu, India.
P. Palani
- Department of Mathematics, Sri Vidya Mandir Arts and Science College, Uthangarai- 636902, Tamil Nadu, India.
Abstract
This paper deals with the Ulam-Hyers stability of the following additive-quadratic mixed type functional equation:
\[
f\left(\frac{u+v}{2}-w\right)+f\left(\frac{v+w}{2}-u\right)+f\left(\frac{w+u}{2}-v\right)
=\frac{7}{8}\left(f(u-v)+f(v-w)+f(w-u)\right)-\frac{1}{8}\left(f(v-u)+f(w-v)+f(u-w)\right)
\]
in paranormed spaces by direct method.
Share and Cite
ISRP Style
S. Karthikeyan, T. R. K. Kumar, S. Vijayakumar, P. Palani, Stabilities and instabilities of additive-quadratic 3D functional equations in paranormed spaces, Journal of Mathematics and Computer Science, 28 (2023), no. 1, 37--51
AMA Style
Karthikeyan S., Kumar T. R. K., Vijayakumar S., Palani P., Stabilities and instabilities of additive-quadratic 3D functional equations in paranormed spaces. J Math Comput SCI-JM. (2023); 28(1):37--51
Chicago/Turabian Style
Karthikeyan, S., Kumar, T. R. K., Vijayakumar, S., Palani, P.. "Stabilities and instabilities of additive-quadratic 3D functional equations in paranormed spaces." Journal of Mathematics and Computer Science, 28, no. 1 (2023): 37--51
Keywords
- Ulam-Hyers stability
- additive functional equation
- quadratic functional equation
- paranormed spaces
MSC
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