Monotonic Function

(redirected from Decreasing operator)

monotonic function

[¦män·ə¦tän·ik ′fəŋk·shən]

Monotonic Function


(or monotone function), a function whose increments Δf(x) = f(x′) − f(x) do not change sign when Δx = x′ − x > 0; that is, the increments are either always nonnegative or always nonpositive. Somewhat inaccurately, a monotonic function can be defined as a function that always varies in the same direction. Different types of monotonic functions are represented in Figure 1. For example, the function y = x3 is an increasing function. If a function f(x) has a derivative f′(x) that is nonnegative at every point and that vanishes only at a finite number of individual points, then f(x) is an increasing function. Similarly, if f′(x) ≤ 0 and vanishes only at a finite number of points, then f(x) is a decreasing function.

Figure 1

A monotonicity condition can hold either for all x or for x on a given interval. In the latter case, the function is said to be monotonic on this interval. For example, the function y = Monotonic Function increases on the interval [−1,0] and decreases on the interval [0, +1]. A monotonic function is one of the simplest classes of functions and is continually encountered in mathematical analysis and the theory of functions. If f(x) is a monotonic function, then the following limits exist for any X0:


References in periodicals archive ?
The former reduces engine noise, in turn decreasing operator fatigue and boosting productivity on jobsites in areas that have noise restrictions.
The T3-MT and T-41 technologies assist Steadicam[TM], Glidecam[TM] and other camera system operators to ride comfortably and safely with the camera attached to the vehicle itself rather than the operator, allowing for flawless content production and decreasing operator fatigue.
By reducing alarms, the solution helps operators notice the most important ones, thereby decreasing operator error.
Patented KIP processes such as High Definition Print Technology and Real Time Thresholding enhance the quality of wide format document production, while decreasing operator effort and overall ownership costs.
WiMAX Forum Certified mobile products will be interoperable, which is key in order to enhance the user experience while decreasing operator investment and consumer costs for broadband anywhere, anytime.
Nortel Networks commitment and contributions to the WiMAX Forum underscore our objective to speed the deployment of advanced broadband service regardless of access choice while decreasing operator costs," said John Hoadley, vice president, advanced technology, Wireless Networks, Nortel Networks.