This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

In this paper, we continue to study convergence problems for a Ishikawa-like iterative process for a finite family of m-accretive mappings. Strong convergence theorems are established in uniformly smooth Banach spaces.

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

Absolutely representing system (ARS) in a Banach space X is a set D ⊂ X such that every vector x in X admits a representation by an absolutely convergent series x = ∑ i aixi with (ai) ⊂ R and (xi) ⊂ D. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via ε-nets of the unit balls. Every ARS in a B-convex Banach ...

In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree. Introduction Let X be a smooth quartic surface in projective three-space P. As a consequence of Nikulin’s theorem [6] X is a Kummer surface if and only if it contains sixteen mutually disjoint smooth rational curves. The classic...

are locally described by classical differential geometry. In case some spatial direction (e.g., the direction of gravity in the natural landscape or the viewing direction in visual space) assumes a special role, this formalism has to be replaced by the special theory of “topographic surfaces’’ and one speaks of “surface relief ’’ (Liebmann, 1902/1927). Examples include topographic relief and— i...

In this paper, we will show that the cost − cosh ◦dHn is a regular cost, meaning that minimizing this cost on hyperbolic space yields a smooth optimal map between two given distributions of mass which satisfies suitable hypotheses. We show this by proving this cost satisfies Ma-Trudinger-Wang’s conditions and by investigating notions of convexity under this cost.

In this paper, the facial expression is mainly focused to achieve the smooth tele-communications. The facial expressions has been considered as a most of the signi cant factors in tele-communications, such as tele-services. To realize the real time facial expression transportation system, we proposed the facial expression space (FES) and a correspondence technique between each personal facial e...