# Hölder condition

(redirected from Holder space)

## Hölder condition

[′hel·dər kən‚dish·ən]
(mathematics)
A function ƒ(x) satisfies the Hölder condition in a neighborhood of a point x0 if |ƒ(x) - ƒ(x0)| ≤ c |(x-x0)| n , where c and n are constants.
A function ƒ(x) satisfies a Hölder condition in an interval or in a region of the plane if |ƒ(x) - ƒ(y)| ≤ c|x - y |nfor all x and y in the interval or region, where c and n are constants.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
A real-valued function f defined on [R.sup.d] belongs to the uniform Holder space [[LAMBDA].sup.[alpha]]([R.sup.d]) ([alpha] > 0) if there exist a constant C and a polynomial P of degree less than a such that
The real-valued function [phi] : [OMEGA] [right arrow] R belongs to the Holder space [H.sup.v]([OMEGA]), with v [member] (0,1), if [there exists] H [member of] R constant, such that
Note that the notion of the f-Holder space includes the standard Holder space [[LAMBDA].sub.[alpha]] by taking f(t) = [t.sup.[alpha]] (so that f([[absolute value of (h)].sup.-1]) = [[absolute value of (h)].sup.-1] = [[absolute value of (h)].sup.-[alpha]]) with 0 < [alpha] [less than or equal to] 1.
Gareth Drake My wife and I have clocked up over 45 years of driving combined and in all that time we have never had a parking ticket until this December when we unknowingly parked in a permit holder space by the outdoor market.
Need to know: You can't rent out a permit holder space and tenants with a parking space can't rent it out.
ON Sunday, September 21, I went shopping at a supermarket in Old Swan, and was very surprised to find the blue badge holder space being used by a well known bread maker to promote its wares.
Kellar says the non-resealable Tetra Prisma is intended to compete with cans for the adult beverage segment, To that end, the package fits in the same drink holder space as a can and offers the same portability--with the added virtue that the Tetra Prisma will bend before it punctures.
Situated on an industrial estate, there is ample free car-parking, including dedicated Blue Badge holder spaces.
Examples of those [X.sub.[alpha]] include, among others, the fractional spaces D([(-A).sup.[alpha]]), the reel interpolation spaces [D.sub.A]([alpha], [infinity]) due to both Lions and Peetre, and the Holder spaces [D.sub.A]([alpha]), which coincide with the continuous interpolation spaces that had been introduced in the literature by Da Prato and Grisvard.
There's a drop off zone for disabled passengers, limited blue badge holder spaces, accessible toilets, electric buggies and manual wheelchairs for loan, Braille and large print guides, hearing loop systems, and paths adapted for wheelchairs.
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