Bull. Korean Math. Soc. -0001; 31(1): 131-138
Printed November 30, -0001
Copyright © The Korean Mathematical Society.
Jaeyoung Chung and Prasanna K. Sahoo
Kunsan National University, University of Louisville
We determine the general solutions $f:\mathbb R^2 \to \mathbb R$ of the functional equation $ f(ux-vy, uy+v(x+y))=f(x, y)f(u, v) $ for all $x, y, u, v\in \mathbb R$. We also investigate both bounded and unbounded solutions of the functional inequality $ |f(ux-vy, uy+v(x+y))-f(x, y)f(u, v)|\le \phi(u, v) $ for all $x, y, u, v\in \mathbb R$, where $\phi:\mathbb R^2 \to \mathbb R_+$ is a given function.
Keywords: exponential type functional equation, general solution, multiplicative function, Proth identity, stability, bounded solution
MSC numbers: 39B82
2023; 60(1): 75-81
2021; 58(3): 603-608
2021; 58(2): 269-275
2018; 55(2): 379-403
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd