# Hölder condition

(redirected from Holder condition)

## 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 ?
The main motivation for considering the case of Holder disturbances is that on one hand the Holder condition generalizes the Lipschitz condition to a larger class of functions without a first-order derivative but having fractional-order derivatives for all orders less than a critical order in turns less than one ; on the other hand, fractional-order derivatives allow us to consider more wider and realistic physical phenomena associated with fractional-order models [15,16] since fractional calculus provides a deeper understanding of the real nature [17,18].
Fractional-order operators provide tools to study nonlocal topological properties of continuous functions, such as their regularity degree in connection with the Holder condition [17,26].
The maximum v such that [phi] complies to the Holder condition (5) is denoted as the critical exponent/order of [phi].
and G(t),g(t),[alpha]'(t) satisfy the Holder condition on [GAMMA] and G(t) [not equal to] 0, [alpha]'(t) [not equal to] 0.
Suppose that the functions G(t) and g(t) satisfy on L the Holder condition, the function [alpha](t) satisfies the Carleman condition (1.2) and [alpha]'(t) [not equal to] 0.
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