Related papers: On approximate cubic homomorphisms

We present sufficient conditions for topological stability of continuous functions $f:\mathbb{R}\to\mathbb{R}$ having finitely many local extrema with respect to averagings by discrete measures with finite supports.

Let $A,B$ be two rings and let $ X$ be an $ A-$module. An additive map $h: A\to B$ is called n-ring homomorphism if $h(\Pi^n_{i=1}a_i)=\Pi^n_{i=1}h(a_i),$ for all $a_1,a_2, ...,a_n \in {A}$. An additive map $D: A\to X$ is called $n$-ring…

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.

We give a procedure to compute the rational homotopy groups of the group of quasi-unitaries of an AF-algebra. As an application, we show that an AF-algebra is K-stable if and only if it is rationally K-stable.

Consider a convex relaxation $\hat f$ of a pseudo-boolean function $f$. We say that the relaxation is {\em totally half-integral} if $\hat f(x)$ is a polyhedral function with half-integral extreme points $x$, and this property is preserved…

The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each "sufficiently rich'' spherical building Y of type W we associate a certain cohomology theory and verify that, first,…

We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the model-theoretic assumption of stability, such a…

We establish the Hyers-Ulam stability of certain linear first-order differential equations with singularities. We then extend these results to higher-order singular linear differential equations that can be written with these first-order…

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

We observe a connection between Cauchy-Schwarz' and Richard's inequalities in inner product spaces and a Ulam-type stability problem for multiplicative Sincov's functional equation. We prove that this equation is super-stable for unbounded…

In this paper, we introduce the idea of $\ast$-homomorphism on a Hilbert $C^{*}$-module. Furthermore, we prove the Hyers-Ulam stability of homomorphisms and $\ast$-homomorphisms on Hilbert $C^{*}$-modules using the fixed point method.

The relation $xy-yx=h(y)$, where $h$ is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach a rigorous meaning to the right-hand side of this equality, we assume that $x$ and $y$ are elements of a…

Using a recently developed $\mathcal H$-calculus we propose a unified approach to the study of rational approximations of holomorphic semigroups on Banach spaces. We provide unified and simple proofs to a number of basic results on…

We study the solutions of the integral Kannappan's and Van Vleck's functional equations $$\int_{S}f(xyt)d\mu(t)+\int_{S}f(x\sigma(y)t)d\mu(t) = 2f(x)f(y), \;x,y\in S;$$ $$\int_{S}f( x\sigma(y)t)d\mu(t)-\int_{S}f(xyt)d\mu(t) = 2f(x)f(y),…

We generalize Wonham's theorem on solvability of algebraic operator Riccati equations to Banach spaces, namely there is a unique stabilizing solution to A*P+PA-PBB*P+C*C=0 when (A,B) is exponentially stabilizable and (C,A) is exponentially…

For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In…

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…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this…

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…