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The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…

We study the decay rate of the energy of solutions to the damped wave equation in a setup where the geometric control condition is violated. We consider damping coefficients which are $0$ on a strip and vanish like polynomials, $x^{\beta}$.…

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x)$ for all $k\in \Bbb N$ and the quartic functional equation…

In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely,…

In this paper, we study the notion of $\phi$-biflatness for some Banach algebras, where $\phi$ is a non-zero multiplicative linear functional. We show that the Segal algebra $S(G)$ is left $\phi$-biflat if and only if $G$ is amenable. Also,…

In this paper we prove that the so--called entropy equation, i.e., \[ H\left(x, y, z\right)=H\left(x+y, 0, z\right)+H\left(x, y, 0\right) \] is stable in the sense of Hyers and Ulam on the positive cone of $\mathbb{R}^{3}$, assuming that…

In this paper, by means of the Gronwall inequality, the {\psi}-Riemann-Liouville fractional partial integral and the {\psi}-Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using these…

In this paper, we provide the sufficient and necessary conditions for the symmetry of the following stable L\'evy-type operator $\mathcal{L}$ on $\mathbb{R}$: $$\mathcal{L}=a(x){\Delta^{\alpha/2}}+b(x)\frac{\d}{\d x},$$ where $a,b$ are the…

The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.

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 are dealing with the solution of the functional equation $$ \varphi\Big(\frac{x+y}2\Big)(f(x)-f(y))=F(x)-F(y), $$ concerning the unknown functions $\varphi,f$ and $F$ defined on a same open subinterval of the reals.…

This paper treats two functional equations, the Kannppan-Van Vleck functional equation $$\mu(y)f(x\tau(y)z_0)\pm f(xyz_0) =2f(x)f(y), \;x,y\in S$$ and the following variant of it $$\mu(y)f(\tau(y)xz_0)\pm f(xyz_0) = 2f(x)f(y), \;x,y\in S,$$…

Let $\mathcal{L}$ be the sub-Laplacian on H-type groups and $\phi: \mathbb{R}^+ \to \mathbb{R}$ be a smooth function. The primary objective of the paper is to study the decay estimate for a class of dispersive semigroup given by…

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and…

We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result…

Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.

We determine the complex-valued solutions of the Kannappan cosine functional law $g(xyz_{0})=g(x)g(y)-f(x)f(y)$, $x,y\in S$, where $S$ is a semigroup and $z_{0}$ is a fixed element in $S.$

We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…

In this paper, by using the orthogonally fixed point method, we prove the Hyers-Ulam stability and the hyperstability of orthogonally 3-Lie homomorphisms for additive $\rho$-functional equation in 3-Lie algebras.\\ Indeed, we investigate…

We study stable solutions to fractional semilinear equations $(-\Delta)^s u = f(u)$ in $\Omega \subset \mathbb{R}^n$, for convex nonlinearities $f$, and under the Dirichlet exterior condition $u=g$ in $\mathbb{R}^n \setminus \Omega$ with…