On the stability of quadratic reciprocal functional equation in non-Archimedean fields (Q2806077)

The authors prove the Hyers-Ulas-Rassias stability of the functional equation NEWLINE\[NEWLINEf((a+1)x+ay)+f((a+1)x-ay)=\frac{2f(x)f(y)((a+1)^2f(y)+a^2f(x))}{((a+1)^2f(y)-a^2f(x))^2}NEWLINE\]NEWLINE in non-Archimedean fields, where \(a\mathbb{Z}\) with \(a\neq 0,-1\). This is a slight generalization of the paper \textit{A. Bodaghi} and \textit{S. O. Kim} [J. Funct. Spaces 2014, Article ID 532463, 5 p. (2014; Zbl 1287.39018)].NEWLINENEWLINE Reviewer's remark: The authors miss to pay attention to the origin of the stability in non-Archimedean setting initiated by the works of \textit{L.M. Arriola} and \textit{W. A. Beyer} [Real Anal. Exch. 31(2005--2006), No. 1, 125--132 (2006; Zbl 1099.39019)] and \textit{M. S. Moslehian} and \textit{Th. M. Rassias} [Appl. Anal. Discrete Math. 1, No. 2, 325--334 (2007; Zbl 1257.39019)].