we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

We study the global structure of moduli spaces of quasi-isogenies of p-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of the p-divisible groups are simple, we compute the cohomology of the moduli space. As an application we determine which moduli spaces are smooth.

In this paper, we will consider the Borel complexity of Pride’s quasi-order p and Pride’s equivalence relation ≈p on the space G of finitely generated groups. Our main results show that these relations are as complex as they conceivably could be.

Given a càdlàg process X on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let Psem be the set of all probability measures P under which X is a semimartingale. We construct processes (B , C, ν ) which are jointly measurable in time, space, and the probability law P , an...

1. Introduction. Combining the work of many people yields a complete quasi-isometry classification of irreducible lattices in semisimple Lie groups (see [F] for an overview of these results). One of the first general results in this classification is the complete description, up to quasi-isometry, of all nonuniform lattices in semisimple Lie groups of rank 1, proved by R. Schwartz [S1]. He show...

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...

It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T0-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top0 of topological T0-spaces and continuous maps is not lower K-true (in the sense of Brümmer...

If 0 < p < 1 we classify completely the linear operators T: Lp -X where X is a p-convex symmetric quasi-Banach function space. We also show that if T: LLo is a nonzero linear operator, then forp < q < 2 there is a subspace Z of Lp, isomorphic to Lq, such that the restriction of T to Z is an isomorphism. On the other hand, we show that if p < q < o, the Lorentz space L(p, q) is a quotient of Lp ...