This paper investigates calculus rules for the limiting Fréchet-subdifferential of infimum value functions of locally Lipschitzian and non-Lipschitzian functions. It is not required that the infimum is attained.

The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let H be a Hilbert space, let C be a nonempty bounded closed convex subset of H, and let M an,k n,k≥1 be a strongly ergodic matrix. If T : C → C is a lipschitzian mapping such that lim infn→∞infm 0,1,... ∑∞ k 1 an,k · ‖Tk m‖ 2 < 2, then the set of fixed points Fix T {...

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and compact path-metric spaces is an map when simply connected. The motivation for such result arises from studying the asymptotic values of BLD-mappings with empty branch set.

We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...

We prove that a sequence of, possibly branched, weak immersions of the two-sphere S into an arbitrary compact riemannian manifold (M, h) with uniformly bounded area and uniformly bounded L−norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S and whose image is made of a connected union of f...

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

We introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping T in the intermediate sense which is necessarily lipschitzian. We establish strong convergence theorem for such method. The result extend and improve the recent ones announced by Inchan and Nammanee, Inchan and concern result of Takahashi, Takeuchi and Kubota [Strong convergence...

Letting $A \subset \mathbb{R}^n$ be Borel measurable and $W_0 : A \to \mathbb{G}(n,m)$ Lipschitzian, we establish that \begin{equation*} \limsup_{r 0^+} \frac{\mathcal{H}^m \left[ \cap B(x,r) (x+ W_0(x))\right]}{\alpha(m)r^m} \geq \frac{1}{2^n}, \end{equation*} for $\mathcal{L}^n$-almost every $x \in A$. In particular, it follows $A$ is $\mathcal{L}^n$-negligible if only $\mathcal{H}^m(A (x+W_0...

Lipschitzian aggregation operators with respect to the natural T indistinguishability operator ET and their powers, and with respect to the residuation → T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be ET -Lipschitzian and → T -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, t...