In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, i...

T norms were introduced by Schweizer and Sklar see e g in the framework of probabilistic metric spaces and are based on a notion used by Menger in or der to extend the triangle inequality in the de nition of metric spaces towards probabilistic metric spaces They have been used extensively for de ning the in tersection of fuzzy sets and for modelling the logical and in fuzzy logic Continuous t n...