Hölder condition

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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.
References in periodicals archive ?
where k is a non-negative, bounded and Holder continuous function such that
We will show that there is a Holder continuous function f on [[omega], dar above], holomorphic on [omega], such that f(p) = 1 while [absolute value of f] < 1 everywhere else on the closure.
T] (S) we denote the spaces of Holder continuous functions and Holder continuous tangential fields (0 < [alpha] < 1), respectively.