Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability to a closed (not necessarily compact)...

The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a-la Johnson–Lindenstrauss fails in any non super reflexive space with non trivial type. We also introduce the concept of Lipschitz (p, r)-summing ma...

In this paper, we first establish a narrow region principle for systems involving the fractional Laplacian in unbounded domains, which plays an important role carrying on direct method of moving planes. Then combining with sliding method, derive monotonicity bounded positive solutions to following Lipschitz domains \begin{document}$...

In this article, we deal with the existence of non-negative solutions class following non local problem $$ \left \{ \textstyle\begin{array}{l} \quad - M\left (\displaystyle \int _{\mathbb{R}^{n}}\int _{\mathbb{R}^{n}} \frac{|u(x)-u(y)|^{\frac{n}{s}}}{|x-y|^{2n}}~dxdy\right ) (-\Delta )^{s}_{n/s} u=\left _{\Omega }\frac{G(y,u)}{|x-y|^{\mu }}~dy \right )g(x,u) \; \text{in}\; \Omega , \\ u =0\quad...

Let $\mathbb{S} \subset \mathbb{C}$ be the circle in plane, and let $\Omega\colon \mathbb{S} \to \mathbb{S}$ an odd bi-Lipschitz map with constant $1+\delta\_\Omega$, where $\delta\_\Omega\geq 0$ is small. Assume also that $\Omega$ twice continuously differentiable. Motivated by a question raised Mattila Preiss, we prove following: If Radon measure $\mu$ has positive lower density finite upper ...

We examine the relationship between infinity harmonic functions, absolutely minimizing Lipschitz extensions, strong absolutely minimizing Lipschitz extensions, and absolutely gradient minimizing extensions in CarnotCarathéodory spaces. Using the weak Fubini property we show that absolutely minimizing Lipschitz extensions are infinity harmonic in any sub-Riemannian manifold.

Remark 1. The Lipschitz condition (4) is called global because it holds for all x, y ∈ R with the same constant L. Klebaner Theorem 5.4 assumes only a local Lipschitz condition, where the Lipschitz constant may depend on the size of x, y. We use a global condition in order to make the presentation simpler. Later on we will also assume a Lipschitz condition with respect to t, see (21). (There is...