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.

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...

We introduce the notion of uniformly refinable map for compact, Hausdorff spaces, as a generalization maps originallydefined metric continua by Jo Ford (Heath) and Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.

In this work, we are concerned with the stability and convergence analysis of second order BDF (BDF2) scheme variable steps for molecular beam epitaxial model without slope selection. We first show that variable-step BDF2 is convex uniquely solvable under a weak time-step constraint. Then it preserves an energy dissipation law if adjacent ratios $r_k:=\tau_k/\tau_{k-1}<3.561.$ Moreover, novel d...