Ulam stability
E85413
Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Ulam stability canonical | 2 |
| Hyers–Ulam stability | 1 |
| Ulam’s stability problem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T718425 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ulam stability Context triple: [Stanislaw Ulam, notableWork, Ulam stability]
-
A.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
-
B.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
C.
Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
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D.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
E.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ulam stability Target entity description: Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
-
A.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
-
B.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
C.
Nyquist stability criterion
The Nyquist stability criterion is a graphical frequency-domain method in control theory used to determine the stability of feedback systems by analyzing how their open-loop transfer function encircles a critical point in the complex plane.
-
D.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
E.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
stability concept in functional equations ⓘ |
| appliesTo |
Cauchy functional equation
ⓘ
Jensen inequality ⓘ
surface form:
Jensen functional equation
additive functional equations ⓘ multiplicative functional equations ⓘ quadratic functional equations ⓘ |
| basisFor | Hyers–Ulam stability theory ⓘ |
| characterizedBy | existence of a bound between approximate and exact solutions ⓘ |
| concerns |
error bounds for approximate solutions
ⓘ
stability of functional equations under perturbations ⓘ |
| coreIdea | approximate satisfaction of a functional equation leads to a nearby exact solution ⓘ |
| defines | conditions under which approximate homomorphisms are close to exact homomorphisms ⓘ |
| field |
functional equations
ⓘ
mathematical analysis ⓘ |
| focusesOn |
approximate solutions of functional equations
ⓘ
existence of exact solutions near approximate ones ⓘ |
| generalizedBy | Hyers–Ulam–Rassias stability ⓘ |
| hasApplication |
stability of derivations
ⓘ
stability of group homomorphisms ⓘ stability of isometries ⓘ stability of linear mappings ⓘ stability of ring homomorphisms ⓘ |
| hasVariant | Hyers–Ulam–Rassias stability ⓘ |
| historicalOrigin | a question posed by Stanisław Ulam in 1940 ⓘ |
| implies | continuous dependence of exact solutions on perturbations ⓘ |
| motivated | study of stability of functional equations ⓘ |
| namedAfter |
Stanislaw Ulam
ⓘ
surface form:
Stanisław Ulam
|
| questionFormulation | whether every approximate solution of a functional equation is near an exact solution ⓘ |
| relatedConcept |
Banach space
ⓘ
approximate homomorphism ⓘ functional inequality ⓘ metric space ⓘ stability of homomorphisms ⓘ |
| relatedTo |
Ulam stability
self-linksurface differs
ⓘ
surface form:
Hyers–Ulam stability
error analysis ⓘ perturbation theory ⓘ stability theory in mathematics ⓘ |
| studiedIn |
nonlinear functional analysis
ⓘ
operator theory ⓘ |
| timePeriod | 20th century mathematics ⓘ |
| typicalSetting |
functional equations between Banach spaces
ⓘ
functional equations between normed spaces ⓘ |
| usedIn |
approximation theory
ⓘ
control theory ⓘ dynamical systems ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ulam stability Description of subject: Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hyers–Ulam stability
this entity surface form:
Ulam’s stability problem