The relationship between directional derivatives of generalized distance functions and the existence of generalized nearest points in Banach spaces is investigated. Let G be any nonempty closed subset in a compact locally uniformly convex Banach space. It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or −1, then the ...

We give quantitative versions of strong convergence results due to Baillon, Bruck and Reich for iterations of nonexpansive odd (and more general) operators in uniformly convex Banach spaces.

We characterize the behavior of a random discrete interface ϕ on [−L,L]d∩Zd with energy ∑V(Δϕ(x)) as L→∞, where Δ is Laplacian and V uniformly convex, symmetric, smooth potential. The called non-Gaussian membrane model. By analyzing Helffer–Sjöstrand representation, associated to Δϕ, we provide unified approach continuous scaling limits rescaled interpolated in dimensions d=2,3, Gaussian approx...

and Applied Analysis 3 In this paper, we firstly present the definition of duality fixed point for a mapping T from E into its dual E∗ as follows. Let E be a Banach space with a single-valued generalized duality mapping Jp : E → E∗. Let T : E → E∗. An element x∗ ∈ E is said to be a generalized duality fixed point of T if Tx∗ Jpx∗. An element x∗ ∈ E is said to be a duality fixed point of T if Tx...

In this article, we investigate the structure of uniformly k $k$ -connected and -edge-connected graphs. Whereas both types have previously been studied independent each other, analyze relations between these two classes. We prove that any graph is also for ≤ 3 $k\le 3$ demonstrate not case > $k\gt . Furthermore, graphs are well understood 2 2$ it known how to construct 3-edge-connected contribu...