Related papers: Solution and Stability of a Mixed Type Functional …
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…
In this article, by using the fixed point method, we prove the generalized Hyers--Ulam stability of biderivations from an algebra to a modular space, associated to bi-additive s-functional inequalities.
In this paper we study the solutions and stability of the generalized Wilson's functional equation $\int_{G}f(xty)d\mu(t)+\int_{G}f(xt\sigma(y))d\mu(t)=2f(x)g(y),\; x,y\in G$, where $G$ is a locally compact group, $\sigma$ is a continuous…
In this paper, we establish the Hyers--Ulam--Rassias stability of ring homomorphisms and ring derivations on fuzzy Banach algebras.
In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…
This paper investigates functional equations arising from perturbations of Cauchy differences. We study equations of the form \[ f(x+y)-f(x)-f(y)=B(x,y) \quad \text{or} \quad f(xy)-f(x)f(y) = B(x,y) \] where $B$ is a biadditive mapping, and…
In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…
Using the $\psi-$Hilfer fractional derivative, we present a study of the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the fractional Volterra integral-differential equation by means of fixed-point method.
In this work, we determine the general solution of the quinquevigintic functional equation and also investigate its stability of this equation in the setting of matrix normed spaces and the framework of matrix non-Archimedean fuzzy normed…
In this work, we prove the existence of integrable solutions for the following generalized mixed-type nonlinear functional integral equation $$x(t)=g\left(t,(Tx)(t)\right)+f\left(t,\int_0^t…
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.
Let $q$ be a prime power. We construct stable polynomials of the form $b^{m-1}(x+a)^m+c(x+a)+d$ over a finite field $\mathbb{F}_{q}$ for $m=2,3,4$ by Capelli's lemma. When $m=3$ and $q$ is even, we confirm the conjecture of Ahmadi and…
In this paper, we consider the existence of normalized solution to the following Kirchhoff equation with mixed Choquard type nonlinearities: \begin{equation*} \begin{cases} -\left(a + b \int_{\mathbb{R}^3} |\nabla u|^2 \, dx\right) \Delta u…
This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stability of closed linear relations in Hilbert spaces.…
Consider the functional equation ${\mathcal E}_1(f) = {\mathcal E}_2(f) ({\mathcal E})$ in a certain framework. We say a function $f_0$ is an approximate solution of $({\mathcal E})$ if ${\mathcal E}_1(f_0)$ and ${\mathcal E}_2(f_0)$ are…
In this paper, we introduce and investigate general 3-variable Jensen $\rho$-functional equation, and prove the Hyers-Ulam stability of the Jensen functional equations associated with the general 3-variable Jensen $\rho$-functional…
In this paper we extend the interior regularity results for stable solutions in [Cabr\'{e}, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] to operators with variable coefficients. We show that stable solutions to the semilinear…
In this paper, we introduce a generalized quadratic functional equation $f(rx + sy) = rf(x) + sf(y) - rsf(x - y)$ where $r, s$ are nonzero real numbers with $r + s = 1.$ We show that this functional equation is quadratic if $r, s$ are…
This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…
We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on…