Ulam stability of a generalized reciprocal type functional equation in non-Archimedean fields (Q889500)

The authors obtain the solution of a generalized reciprocal-type functional equation in two variables of the form \[ r(x+y)=\frac{kr(x+(k-1)y)r((k-1)x+y)}{r(x+(k-1)y)+r((k-1)x+y)} \] in non-Archimedean fields, where \(k>2\) is a positive integer. They also investigate the generalized Hyers-Ulam-Rassias stability of the above functional equation controlled by a mixed product-sum of powers of norms.