منابع مشابه
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.
متن کاملProjective Convexity in P Implies Grassmann Convexity
In this note we introduce the notion of Grassmann convexity analogous to the wellknown notion of convexity for curves in real projective spaces. We show that the curve in G2,4 osculating to a convex closed curve in P is Grassmann-convex. This proves that the tangent developable (i.e. the hypersurface formed by all tangents) of any convex curve in P has the ‘degree’ equal to 4. Here by ‘degree’ ...
متن کاملOn 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...
متن کاملUniform 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.
متن کاملNearly Uniform Convexity of Infinite Direct Sums
Those kinds of infinite direct sums are characterized for which NUC (NUS, respectively) is inherited from the component spaces to the direct sum. 1. NUC and the lower KK-modulus. The Banach space X is said to be nearly uniformly convex, abbreviated NUC (cf. [2]), if: for every ε > 0, there exists δ > 0 such that the convex hull conv{xn} of every sequence {xn} in the unit ball BX of X with separ...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Sciences and Applications
سال: 2017
ISSN: 2008-1898,2008-1901
DOI: 10.22436/jnsa.010.10.15