A fixed point approach to the stability of functional equations in non-Archimedean metric spaces (Q642548)

Let \(X\) be an arbitrary set, \(Y\) be a complete ultrametric space, \(f_1,\dots ,f_k:\;X\to X\), \(\Phi:\;X\times Y^k\to Y\). The authors find conditions for the solvability of the functional equation \(\Phi (x,\psi (f_1(x)),\dots ,\psi (f_k(x)))=\psi (x)\), \(x\in X\) (with respect to \(\psi:\;X\to Y\)) and its generalizations. The result, in the spirit of the Hyers-Ulam stability where a solution is obtained as a limit of approximate solutions, is based on a new fixed point theorem.