The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

In this paper, we investigate the Hyers-Ulam stability of the orthogonally  cubic equation and  Pexiderized cubic equation [f(kx+y)+f(kx-y)=g(x+y)+g(x-y)+frac{2}{k}g(kx)-2g(x),]in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the  $2$-variables cubic  equation [ f(2x+y,2z+t)+f(2x-y,2z-t) =2...

Problem 1.1. Given a metric group (G,·,d), a positive number ε, and a mapping f : G→ G which satisfies the inequality d( f (xy), f (x) f (y)) ≤ ε for all x, y ∈ G, do there exist an automorphism a of G and a constant δ depending only on G such that d(a(x), f (x)) ≤ δ for all x ∈G? If the answer to this question is affirmative, we say that the equation a(xy) = a(x)a(y) is stable. A first answer ...

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associated to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, prove an existence result. We also investigate the uniqueness solution using Banach contraction principle. Moreover, study Ulam-Hyers stability and generalized-Ulam-Hyers solutions. Some illustrative examples are presented.

In the present paper we study the Ulam-Hyers stability of some elliptic partial differential equations on bounded domains with Lipschitz boundary. We use direct techniques and also some abstract methods of Picard operators. The novelty of our approach consists in the fact that we are working in Sobolev spaces and we do not need to know the explicit solutions of the problems or the Green functio...

the main goal of this paper is the study of the generalized hyers-ulam stability of the following functionalequation f (2x  y)  f (2x  y)  (n 1)(n  2)(n  3) f ( y)  2n2 f (x  y)  f (x  y)  6 f (x) where n  1,2,3,4 , in non–archimedean spaces, by using direct and fixed point methods.

This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations impulse. Further, by using techniques of nonlinear functional analysis, we study Ulam-Hyers-Rassias stability.

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.