R. Kalaichelvan - Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603 203, Tamil Nadu, India. U. Jayaraman - Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur - 603 203, Tamil Nadu, India. P. S. Arumugam - Department of Mathematics, Kings Engineering College, Irungattukottai, Sriperumbudur, Chennai - 602 117, Tamil Nadu, India.
The main aim of this paper is to establish the generalized Hyers-Ulam stability of a bi-quadratic mappings in non-Archimedean spaces. That is, we prove the generalized Hyers-Ulam stability of a bi-quadratic functional equation of the form \begin{eqnarray} && f(a_{1}(x_{1}+x_{2}),b_{1}(y_{1}+y_{2}))+f(a_{2}(x_{1}+x_{2}),b_{2}(y_{1}-y_{2})) +f(a_{3}(x_{1}-x_{2}),b_{3}(y_{1}+y_{2})) f(a_{4}(x_{1}-x_{2}),b_{4}(y_{1}-y_{2})) \\& =& C_{11}f(x_{1},y_{1})+C_{12}f(x_{1},y_{2})+C_{21}f(x_{2},y_{1})+C_{22}f(x_{2},y_{2}) \end{eqnarray} in non-Archimedean Banach spaces using Hyers direct method.
R. Kalaichelvan, U. Jayaraman, P. S. Arumugam, Generalized Hyers-Ulam stability of a bi-quadratic mapping in non-Archimedean spaces, Journal of Mathematics and Computer Science, 31 (2023), no. 4, 393--402
Kalaichelvan R., Jayaraman U., Arumugam P. S., Generalized Hyers-Ulam stability of a bi-quadratic mapping in non-Archimedean spaces. J Math Comput SCI-JM. (2023); 31(4):393--402
Kalaichelvan, R., Jayaraman, U., Arumugam, P. S.. "Generalized Hyers-Ulam stability of a bi-quadratic mapping in non-Archimedean spaces." Journal of Mathematics and Computer Science, 31, no. 4 (2023): 393--402