Banach spaces have been given by Edelstein but under hypotheses on the existence of strong limit points for the sequence I Unx I which are difficult to verify. Cf. Edelstein, M., "On fixed and periodic points under contractive mappings," J. London Math. Soc., 37, 74-79 (1962), "On nonexpansive mappings of Banach spaces," Proc. Cambridge Philos. Soc., 60, 439-447 (1964). 9 Added in proof: After ...

A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while welldefined, is not continuous. Space-filling curves, the finite approximations to space-filling functions, have found application in global optimization, database indexing, and dimension reduction among oth...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...

If u 7→ A(u) is a C1,α-mapping having as values unbounded selfadjoint operators with compact resolvents and common domain of definition, parametrized by u in an (even infinite dimensional) space then any continuous arrangement of the eigenvalues u 7→ λi(u) is C0,1 in u. If u 7→ A(u) is C0,1, then the eigenvalues may be chosen C0,1/N (even C0,1 if N = 2), locally in u, where N is locally the max...

A high-spatial-resolution coherent Doppler wind lidar (CDWL) with high modulation efficiency is reported. The pseudo-random phase coding (PRPC) links the spatial resolution to rate but suffers from non-rectangular transition caused by limited bandwidth. With help of continuous (CPM), abrupt switching between successive bit intervals avoided, thus significantly reducing bandwidth requirement. By...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...