Chebyshev centers and uniform convexity

On the Uniform Convexity Of

The standard proof of the uniform convexity of L using Clarkson’s [1] or Hanner’s [2] inequalities (see also [4]) is rarely taught in functional analysis classes, in part (the author imagines) because the proofs of those inequalities are quite non-intuitive and unwieldy. We present here a direct proof, cheerfully sacrificing the optimal bounds – for which, see [2, 4]. It fits quite nicely in wi...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules

Uniform Estimates and Convexity in Capillary Surfaces

We prove uniform convexity of solutions to the capillarity boundary value problem for fixed boundary angle in (0, π/2) and strictly positive capillarity constant provided that the base domain Ω ⊂ R is sufficiently close to a disk in a suitable C-sense.

The Chebyshev selections and fixed points of set-valued mappings in Banach spaces with some uniform convexity

Keywords: Set-valued mapping Chebyshev center Uniformly convex Locally uniformly convex Chebyshev fixed point a b s t r a c t The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and th...

POWER TYPE UNIFORM CONVEXITY OF X VIA p - ASYMPTOTIC UNIFORM CONVEXITY OF L r ( X

We show that if Lr(X), 1 < r < ∞, has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type.