In the present paper we derive criteria for upper Lipschitz/Hőlder continuity of the set of minimal points of a given subset A ⊂ Y of a normed space Y when A is subjected to perturbations. To this aim we introduce the rate of containment of A, a real-valued function of one real variable, which measures the depart from minimality as a function of the distance from the minimal point set. The main...

We prove regularity (i.e., smoothness) of measures on R d satisfying the equation L = 0 where L is an operator of type Lu = tr(Au 00) + B ru. Here A is a Lipschitz continuous, uniformly elliptic matrix-valued map and B is merely-square integrable. We also treat a class of corresponding innnite dimensional cases where IR d is replaced by a locally convex topological vector space X. In this cases...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

We consider a new approach to approximate stability analysis for tri-additive functional inequality and obtain the optimal approximation permuting tri-derivations tri-homomorphisms in unital matrix algebras via vector-valued alternative fixed-point theorem, which is popular technique of proving equations. also present small list aggregation functions on classical, well-known special investigate...

A spectral function on a formally real Jordan algebra is a real-valued function which depends only on the eigenvalues of its argument. One convenient way to create them is to start from a function f : R 7→ R which is symmetric in the components of its argument, and to define the function F (u) := f(λ(u)) where λ(u) is the vector of eigenvalues of u. In this paper, we show that this construction...

For 1 2 < α < 1, we propose the MDP analysis for family S α n = 1 n α n i=1 H(Xi−1), n ≥ 1, where (Xn) n≥0 be a homogeneous ergodic Markov chain, Xn ∈ R d , when the spectrum of operator Px is continuous. The vector-valued function H is not assumed to be bounded but the Lipschitz continuity of H is required. The main helpful tools in our approach are Poisson's equation and Stochastic Exponentia...

In nonlinear programming, the strong second-order optimality condition and the linearly independent gradient condition have many uses. In particular, the first guarantees that a point is an isolated locally optimal solution, while the second insures the uniqueness of the associated multiplier vector, but other, less stringent assumptions would already be enough for that. In fact, the combinatio...

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles quantum differential coming from the 3-D calculus of Woronowicz on SUq(2) . The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fiber, associated quantum vector...

We extend the notion of ascent and descent for an operator acting on a vector space to sets of operators. If the ascent and descent of a set are both finite then they must be equal and give rise to a canonical decomposition of the space. Algebras of operators, unions of sets and closures of sets are treated. As an application we construct a Browder joint spectrum for commuting tuples of bounded...

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical “square” of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and the Malvenuto-Reutenauer Hopf algebra of per...