Monotonic Function

(redirected from Monotone increasing)

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 ?
i) monotone increasing, as l increases, while EY < P < P,
q [member of] Q] be monotone increasing collections of an intuitionistic Fuzzy smooth quasi uniform decreasing open [F.
r [member of] Q] are monotone increasing families of an intuitionistic Fuzzy smooth quasi uniform decreasing open [F.
The monotone increasing top segment exists if and only if [Q.
GAMMA](s) exist the least value in open interval [1,2], and monotone decreasing at the left side of the point, at the right side of the point monotone increasing.
Thus we have two monotone increasing families of soft L-fuzzy BV closed open [G.
1] is a monotone increasing bijective mapping'Cand [[phi].
is a monotone increasing function such that [psi](0) = 0 and [psi]: [R.
ii) [xi] = [xi](x) is a monotone increasing function about x;
In Imoru and Olatinwo [12], the following contractive definition was employed: there exist a [member of] [0,1) and a monotone increasing function [partial derivative]: [R.
must be a strictly monotone increasing sequence, where [[sigma].