holder$35520$ - translation to ελληνικό
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holder$35520$ - translation to ελληνικό

TYPE OF CONTINUITY OF A COMPLEX-VALUED FUNCTION
Holder continuous; Holder condition; Holder space; Hölder space; Hölder continuity; Hölder continuous function; Holder continuous function; Hölder class; Hölder continuous; Holder class; Holder continuity; Hoelder condition; Hoelder norm; Hölder norm; Holder norm; Hoelder space; Hoelder continuous function; Hoelder continuous; Hoelder class; Hoelder continuity; Hölder-continuous function; Holder function; Hölder seminorm; Hölder exponent; Holder exponent; Hölder assumption; Hölder spaces; Local Hölder continuity; Local Holder continuity; Locally Hölder continuous; Locally Holder continuous; Locally Hölder continuous function; Locally Holder continuous function

holder      
n. κρατών, κάτοχος
pen holder         
WIKIMEDIA DISAMBIGUATION PAGE
Pen holder; Penholder (disambiguation)
κοντυλοφόρος
season ticket         
Season ticket holder; Season-ticket; Dedicated season ticket holder; Season pass; Season Ticket; Season Pass; Season pass (winter sports)
εισιτήριο διάρκειας

Ορισμός

Holder
·noun One who, or that which, holds.
II. Holder ·noun One who is employed in the hold of a vessel.
III. Holder ·noun One who holds land, ·etc., under another; a tenant.
IV. Holder ·noun The payee of a bill of exchange or a promissory note, or the one who owns or holds it.

Βικιπαίδεια

Hölder condition

In mathematics, a real or complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants C ≥ 0, α > 0, such that

| f ( x ) f ( y ) | C x y α {\displaystyle |f(x)-f(y)|\leq C\|x-y\|^{\alpha }}

for all x and y in the domain of f. More generally, the condition can be formulated for functions between any two metric spaces. The number α is called the exponent of the Hölder condition. A function on an interval satisfying the condition with α > 1 is constant. If α = 1, then the function satisfies a Lipschitz condition. For any α > 0, the condition implies the function is uniformly continuous. The condition is named after Otto Hölder.

We have the following chain of strict inclusions for functions over a closed and bounded non-trivial interval of the real line:

Continuously differentiableLipschitz continuousα-Hölder continuousuniformly continuouscontinuous,

where 0 < α ≤ 1.