In this paper, we study the Hyers-Ulam stability with respect to linear differential condition of fourth order. Specifically, treat ${\psi}$ as an interact arrangement condition, i.e., $ \begin{align*} {\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} {\xi}_3 {\psi}' {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa}) \end{align*} $ where ${\psi} \in c^...

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...

In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order.

We will consider the Banach space valued differential equation y′(t) = Ay(t) , where A is an n× n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y(n)(t) + an−1y(n−1)(t) + · · ·+ a1y′(t) + a0y(t) = 0 has the Hyers-Ul...

In this paper, we investigate the Hyers-Ulam stability of additive functional equations of two forms: of “Jensen” and “Jensen type” in the framework of multi-normed spaces. We therefore provide a link between multi-normed spaces and functional equations. More precisely, we establish the Hyers-Ulam stability of functional equations of these types for mappings from Abelian groups into multi-norme...

*Correspondence: [email protected]; [email protected] 2Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 3Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, 660-701, Korea Full list of author information is available at the end of the article Abstract In this paper, we establish the generalized Hyers-Ulam stability problem of...

Copyright q 2010 Dongseung Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function f...

In this paper, we establish the Hyers–Ulam–Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.

In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brzc{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements and generalizations of the main result of M. Piszczek and J. Szczawi'{n}ska [21].