for given functions

USAGE SUMMARY

The phrase "for given functions" is correct and usable in written English.
It can be used in mathematical or programming contexts to refer to specific functions that have been defined or established. Example: "The results hold true for given functions in the specified domain."

✓ Grammatically correct

Science

Mathematical Sciences

Fixed Point Theory and Applications

Advances in Difference Equations

Biomedical Optics Express

Plosone

Human-verified examples from authoritative sources

Exact Expressions

5 human-written examples

In this paper some results about the Hyers-Ulam-Rassias stability for thelinear functional equations in general form and its Pexiderized can beproved for given functions on general domain to a complex Banach spacesunder some suitable conditions.

Mathematical Sciences

where (2.2). holds for all and for given functions.

Fixed Point Theory and Applications

where is defined as in the beginning of Section 2, is strictly increasing odd function satisfying for, satisfies (4.2). for given functions and   satisfying for, and functions and satisfy that.

Advances in Difference Equations

The neuropsychological approach in patients with brain lesions is of clear value in establishing the necessity of brain areas for given functions.

Plosone

For given functions ρ (R̄2), f, and g(R1, R2, R̄1, R̄2), it is always possible to find the optimal nanoshell radii, R ¯ 1 opt and R ¯ 2 opt, which ensure that the photothermal therapy is the most efficient under the circumstances.

Biomedical Optics Express

Human-verified similar examples from authoritative sources

Similar Expressions

55 human-written examples

For given function, we set.

Advances in Difference Equations

For given function (u_{k}in H_{h}), we have the following inequality on each triangular element (ein S_{h}): vert nabla w_{0} vert le vert nabla u_{k} vert ^{p-1}.

Journal of Inequalities and Applications

For those given functions, the problem has a unique solution u_{ex} (x,t,s )=e^{-2t-s}sin x. (18).

Journal of Inequalities and Applications

For convenience, for a given function ξ ∈ L∞[0, T], we denote the essential supremum and infimum of ξ by ξ* and ξ*, respectively.

Advances in Difference Equations

A method for determining function (mathsf{G}(m,k)) for a given function (mathsf{F}(m,k)) can be found in [17].

Journal of Inequalities and Applications

The necessary condition for to possess an extremum for a given function is that satisfies the following -Euler-Lagrange equations: (53).

Advances in Difference Equations

Expert writing Tips

Best practice

When using "for given functions", ensure that the functions have been clearly defined or are well-understood within the context of your writing. This avoids ambiguity and ensures clarity for the reader.

Common error

A common mistake is using the phrase "for given functions" without actually specifying or making clear what those functions are. Always provide context or a clear reference to the functions you are discussing.

Linguistic Context

The phrase "for given functions" acts as a prepositional phrase that modifies a statement or theorem, limiting its scope to a specific set of functions. It sets the context by indicating that the following statement applies only to those functions that have been previously defined or are assumed to be known. As confirmed by Ludwig, this is a correct and usable phrase.

Expression frequency: Rare

Frequent in

Science

80%

Academia

10%

Formal & Business

5%

Less common in

News & Media

2%

Encyclopedias

2%

Wiki

1%

Ludwig's WRAP-UP

In summary, the phrase "for given functions" is grammatically sound and primarily used in formal, scientific contexts. As confirmed by Ludwig, it is used to define the scope of a statement by referring to functions that have been clearly defined. The phrase is relatively rare, so it's essential to provide clear definitions of the functions to avoid ambiguity. Alternatives like "for specified functions" can be used to emphasize the precision of the definitions. While correct, ensure the "given functions" are properly introduced for clarity and context.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

for specified functions

Replaces "given" with "specified", implying that the functions are precisely defined beforehand.

with predetermined functions

Uses "predetermined" to emphasize that the functions are established in advance.

using defined functions

Substitutes "given" with "defined", highlighting that the functions have established definitions.

considering pre-existing functions

Employs "pre-existing" to stress that the functions are already available or known.

for established functions

Replaces "given" with "established", indicating that the functions are well-recognized and accepted.

with prescribed functions

Utilizes "prescribed" to suggest that the functions are set by a rule or authority.

for designated functions

Uses "designated" to indicate that the functions have been specifically assigned or chosen.

under known functional conditions

Phrases the concept in terms of 'functional conditions' that are already known.

assuming provided functions

Uses "provided" to imply that the functions are supplied or made available.

when using available functions

Focuses on the availability of the functions being used, rather than their given nature.

FAQs

How can I use "for given functions" in a sentence?

You can use "for given functions" to specify the conditions or assumptions under which a particular result or method applies. For example: "The theorem holds true for given functions that are continuous and differentiable."

What is a more formal way to say "for given functions"?

A more formal alternative is "for specified functions", which emphasizes that the functions are precisely defined beforehand.

In what contexts is "for given functions" typically used?

This phrase is commonly used in mathematical, scientific, and technical writing, where it's essential to establish clear conditions and assumptions.

Is there a difference between "for given functions" and "for any functions"?

Yes. "For given functions" refers to a particular set of functions that are already defined or specified, while "for any functions" implies a general statement that applies to all possible functions within a certain class or domain.