an increasing operator

USAGE SUMMARY

The phrase "an increasing operator" is correct and usable in written English.
It can be used in mathematical or programming contexts to describe an operator that produces a larger output as the input increases. Example: "In this function, we define an increasing operator that ensures the output value rises with each increment of the input."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

47 human-written examples

An operator (Phi: mathbb{C}rightarrowmathbb{E}) is said to be an increasing operator if begin{aligned} x, yinmathbb{C},quad xpreceq yquad Rightarrowquad Phi xpreceqPhi y. end{aligned} Similarly, An operator (Phi: mathbb{C}rightarrowmathbb{E}) is called a decreasing operator if begin{aligned} x, yinmathbb{C},quad xpreceq yquad Rightarrowquad Phi xsucceqPhi y. end{aligned}.

Boundary Value Problems

Hence T is an increasing operator.

Advances in Difference Equations

Therefore, T is an increasing operator.

Advances in Difference Equations

(A Krightarrow K) is an increasing operator.

Advances in Difference Equations

Finally, we assert that is an increasing operator.

Boundary Value Problems

Hence maps into and is an increasing operator.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

13 human-written examples

We consider a monotone increasing operator in an ordered Banach space having u − and u + as a strong super- and subsolution, respectively.

Fixed Point Theory and Applications

Assume that is a normal solid cone in a real Banach space and is a -concave increasing operator.

Boundary Value Problems

It follows from assumption (H1) that Q : D → C ( R +, E ) is a continuously increasing operator.

Advances in Difference Equations

From condition (H2), we have that N + J − 1 P : K ∩ dom ( L ) → K 1 is a monotone increasing operator.

Boundary Value Problems

From Theorem 4.1 we know that (Q_{2}:[v_{0},w_{0}]rightarrow[v_{0},w_{0}]) is a continuously increasing operator.

Advances in Difference Equations

Expert writing Tips

Best practice

When using "an increasing operator", clearly define the domain and codomain of the operator and the ordering used. This will ensure clarity and prevent ambiguity.

Common error

A common mistake is to assume that "an increasing operator" necessarily implies a linear relationship. Remember that the operator only needs to preserve the order, not necessarily scale the input linearly. For example, a logarithmic function over positive values can be "an increasing operator".

Linguistic Context

The phrase "an increasing operator" functions as a noun phrase that identifies a specific type of mathematical operator. It defines an operator's behavior in terms of order preservation. Ludwig AI confirms this usage across scientific publications.

Expression frequency: Common

Frequent in

Science

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Less common in

News & Media

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Formal & Business

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Encyclopedias

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Ludwig's WRAP-UP

In summary, the phrase "an increasing operator" is a common term used in scientific and mathematical contexts to describe an operator that preserves the order of its inputs. According to Ludwig AI, its usage is grammatically correct. The phrase is most frequently found in scientific literature and has a formal and scientific register. To ensure clarity, it's best practice to define the domain and ordering clearly. Be cautious not to assume linearity when using this term.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

monotonically increasing operator

This alternative adds the qualifier 'monotonically' emphasizing the consistent direction of the increase.

non-decreasing operator

This term avoids strict increase, allowing for the possibility of the operator's output remaining constant.

increasing function

This phrase replaces "operator" with the more general term "function".

monotone operator

This is a more general term that encompasses both increasing and decreasing operators.

order-preserving operator

This highlights the operator's characteristic of maintaining the order of inputs.

growth-inducing operator

This alternative emphasizes the growth aspect of the operator's function.

amplifying operator

This describes the operator's behavior as something that enlarges or boosts its input.

enhancing operator

This term highlights the operator's role in improving or augmenting its input.

scaling operator

This refers to an operator that changes the magnitude of its input.

positive operator

This is more general, indicating that the operator preserves positivity.

FAQs

What does "an increasing operator" mean in mathematics?

In mathematics, "an increasing operator" refers to a function or transformation that preserves order. If x ≤ y, then T(x) ≤ T(y) where T is the operator.

How does "an increasing operator" differ from a strictly increasing operator?

While "an increasing operator" (also known as a non-decreasing operator) allows for the possibility that T(x) = T(y) even when x < y, a strictly increasing operator requires that T(x) < T(y) whenever x < y.

In what contexts is the concept of "an increasing operator" commonly used?

The concept of "an increasing operator" is frequently used in functional analysis, operator theory, and the study of differential equations, particularly when analyzing the existence and uniqueness of solutions.

Can you provide examples of operators that are not "increasing operators"?

Examples of operators that are not "increasing operators" include decreasing operators (where the order is reversed), and operators that do not consistently preserve or reverse the order (e.g., operators with oscillating behavior).