In this paper, we investigate the generalized Hyres–Ulam–Rassias stability and Bourgin-type superstability of higher derivations in non-Archimedean Banach algebras by using a version of fixed-point theorem.

In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations.

We say that a functional equation (ξ) is stable if any function g satisfying the functional equation (ξ) approximately is near to a true solution of (ξ). In this paper, by using Banach's contraction principle, we prove the stability of nonlinear partial differential equations of the following forms:p(x, t)y xx (x, t) + q(x, t)y x (x, t) = f (x, t, y(x, t)).

We investigate the superstability of generalized derivations in non-Archimedean algebras by using a version of fixed point theorem via Cauchy functional equation.

We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation. Abstract and Applied AnalysisNA 1 x 0 if and only if x 0;NA 2 rx |r| x for all r ∈ K and x ∈ X;NA 3 x y ≤ max{ x , y } for all x, y ∈ X the strong triangle inequality .Then, X, · is called a non-Archimedean normed space.