The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalit...

Earlier work (Hammond, 1988a, b) on dynamically consistent “consequentialist” behaviour in decision trees was unable to treat zero probability events satisfactorily. Here the rational probability functions considered in Hammond (1994), as well as other non-Archimedean probabilities, are incorporated into decision trees. As before, the consequentialist axioms imply the existence of a preference ...