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Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $\lambda$, we study Hyers-Ulam stability of the global differential equation $Vy=\lambda…

Analysis of PDEs · Mathematics 2017-05-26 Maysam Maysami Sadr

Hyre-Ulam stability of functional equation in single variable is studied in non-triangular metric spaces. We derive it as applications of some fixed point results developed on the said structure. A general version of Baker's theorem is also…

Functional Analysis · Mathematics 2024-05-22 Supriti Laha , Lakshmi Kanta Dey

We show that noncommutative analog of additive functional equation has Hyers-Ulam stability on amenable discrete quantum (semi)groups. This generalizes an old classical result.

Operator Algebras · Mathematics 2015-06-23 Maysam Maysami Sadr

Hyers-Ulam stability of the difference equation with the initial point $ z_0 $ as follows $$ z_{i+1} = \frac{az_i + b}{cz_i + d} $$ is investigated for complex numbers $ a,b,c $ and $ d $ where $ ad - bc = 1 $, $ c \neq 0 $ and $a + d \in…

Dynamical Systems · Mathematics 2017-08-30 Young Woo Nam

The generalized Hyers--Ulam--Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.

Functional Analysis · Mathematics 2021-07-23 Mohammad Sal Moslehian

In this paper, we discuss the Hyers-Ulam stability of closable (unbounded) operators with several interesting examples. We also present results pertaining to the Hyers-Ulam stability of the sum and product of closable operators to have the…

Functional Analysis · Mathematics 2024-03-12 Arup Majumdar , P. Sam Johnson , Ram N. Mohapatra

In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in…

Classical Analysis and ODEs · Mathematics 2013-07-03 Zoltán Boros , Eszter Gselmann

In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.

Functional Analysis · Mathematics 2015-12-16 Soon-Mo Jung , Dorian Popa , Michael Th. Rassias

In this work, we prove an existence theorem of the Hyers-Ulam stability for the nonlinear Volterra integral equations which improves and generalizes Castro-Ramos theorem by using some weak conditions.

Functional Analysis · Mathematics 2015-03-30 Wei-Shih Du

In present paper, we establish sufficient conditions for existence and stability of solutions for system of nonlinear implicit fractional differential equations. The main techniques are based on method of successive approximations. Finally,…

Classical Analysis and ODEs · Mathematics 2017-07-25 D. B. Dhaigude , Sandeep P. Bhairat

In this paper, we study Hyers-Ulam stability for integral equation of Volterra type in time scale setting. Moreover we study the stability of the considered equation in Hyers-Ulam-Rassias sense. Our technique depends on successive…

Dynamical Systems · Mathematics 2017-01-06 Alaa E. Hamza , Ahmed G. Ghallab

This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating…

Functional Analysis · Mathematics 2025-08-15 Jing Zhang , Qi Liu , Yongmo Hu , Linlin Fu , Yuxin Wang , Jinyu Xia , John Michael Rassias , Choonkil Park , Yongjin Li

The purpose of this paper is to summarize the recent results on the stability of the parametric fundamental equation of information. Furthermore, by the help of a modification of a method we used in \cite{GM08} we shall give a unified proof…

Classical Analysis and ODEs · Mathematics 2013-07-03 Eszter Gselmann

The primary objective of this paper is to introduce Hyers-Ulam-type stability results for monotone, subadditive, and convex graphs. We consider their standard definitions in an approximate sense and demonstrate the existence of a…

General Mathematics · Mathematics 2026-02-05 Angshuman R. Goswami , Mahmood K. Shihab

This study deals with the Ulam stability of non-autonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional…

Classical Analysis and ODEs · Mathematics 2023-07-31 Douglas R. Anderson , Masakazu Onitsuka , Donal O'Regan

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…

Classical Analysis and ODEs · Mathematics 2008-12-19 Yifei Pan , Mei Wang

More than 20 years after Fickett attempted to prove the Hyers-Ulam stability of isometries defined on bounded subsets of $\mathbb{R}^n$ in 1981, V\"{a}is\"{a}l\"{a} improved Fickett's result significantly. In this paper, we will improve…

Functional Analysis · Mathematics 2021-05-04 Soon-Mo Jung

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} \phi(x+y-z)+\phi(x+z-y)+\phi(y+z-x)=\phi (x-y)+\phi(x-z)+\phi(z-y) +\phi(x)+\phi(y) +\phi(z) \end{multline*} in modular space, with or without…

Functional Analysis · Mathematics 2025-05-14 Abderrahman Baza , Mohamed Rossafi , Arul Joseph Gnanaprakasam

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $\Psi$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam--Hyers…

Dynamical Systems · Mathematics 2020-12-17 Kishor D. Kucche , Jyoti P. Kharade