Related papers: Solution and Stability of a Mixed Type Functional …
By means of the recent $\psi$-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias on closed intervals $[a,b]$ and $[a,\infty)$ for a…
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.
The aim of this paper is to study Hyers-Ulam-Rassias stability for a Volterra-Hammerstein functional integral equation in three variables via Picard operators.
In this paper, we study the regularity of solutions to a linear elliptic equation involving a mixed local-nonlocal operator of the form $$Lu - \operatorname{div}\big(a(x)\nabla u(x)\big)= f, \quad \text{in } \Omega \subset \mathbb{R}^n,$$…
In this paper, we introduce the concept of j-hom-derivation, $j\in\{1,2\}$ and solve the new generalized additive-quadratic functional equations in the sense of ternary Banach algebras. Moreover, using the fixed point method, we prove its…
The main purpose of this paper is to determine the solution of generalized convex set-valued mappings satisfying certain functional equation. Some conclusions of stability of set-valued functional equations are obtained.
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…
Addressing stability in functional equations is a critical task with broad implications across mathematics and its applications. In this paper, we present a novel direct method for proving the stability of the following equation,…
We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and…
In this paper, we investigate Jordan *-homomorphisms on $C^*$-algebras associated with the following functional inequality $\|f(\frac{b-a}{3})+f(\frac{a-3c}{3})+f(\frac{3a+3c-b}{3})\| \leq \|f(a)\|.$ We moreover prove the superstability and…
The generalized Hyers--Ulam--Rassias stability of generalized derivations on unital Banach algebras into Banach bimodules is established.
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…
This paper studies a nonlinear fractional implicit differential equation (FIDE) with boundary conditions involving a HilferHadamard type fractional derivative. We establish the equivalence between the Cauchy-type problem (FIDE) and its…
In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative.…
We present a stable and convergent mixed finite element method (MFEM) for the linear regularized 13-moment (R13) equations in rarefied gas dynamics. Unlike existing methods that require stabilization via penalty terms, our scheme achieves…
We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions. Moreover, when h is…
Using Gronwall inequality we will investigate the Ulam-Hyers and generalized Ulam-Hyers-Rassias stabilities for the solution of a fractional order pseudoparabolic partial differential equation.
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…
In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…
We introduce a new concept of Hyers-Ulam stability, in which in the size of a pseudosolution of a given ordinary differential equation and its deviation from an exact solution are measured with respect to different norms. These norms are…