Stability of Davison functional equation with \(n\)- variables over non-Archimedean \((n, \beta)\) normed spaces

Volume 35, Issue 4, pp 492--502 https://dx.doi.org/10.22436/jmcs.035.04.08

Publication Date: June 13, 2024 Submission Date: March 13, 2024 Revision Date: May 10, 2024 Accteptance Date: May 19, 2024

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Authors

K. D. Sankar - Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, India. S. Sampath - Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur-603 203, India.

Abstract

In this paper, we discuss the Hyers-Ulam stability of the Davison functional equation \[ \sum_{i=1}^{n-1}m(x_ix_n)+\sum_{i=1}^{n-1}m(x_i+x_n)=\sum_{i=1}^{n-1}m(x_ix_n+x_i)+m(x_n) \] with \(n\)-variables over non-Archimedean \((n, \beta)\) normed spaces (NAn\(\beta\)NS). Also, discuss some results for the same with suitable counter-example.

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Keywords

• Hyers-Ulam stability
• Davison functional equation
• non-Archimedean \((n, \beta)\) normed spaces (NAn\(\beta\)NS)

MSC

•  39B82
•  39B72
•  12J25

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