for all u [greater than or equal to] v and m [less than or equal to] 0, but [??](u) is neither weakly fuzzy pseudoinvex

monotone function nor weakly fuzzy quasi-invex

monotone function.

From this point on, speaking of a diagonally

monotone function [PHI], we always assume that the respective index J,

However, the concept closely relates to that of nowhere

monotone functions. Indeed, suppose that f is a nowhere

monotone function of bounded variation on [0,1].

Many mathematicians may never have heard of Bernstein functions, because in probability they are known as Laplace exponents, in harmonic analysis as negative definite functions, in complex analysis as Pick or Nevanlinna functions, and in matrix analysis and operator theory as

monotone function. Schilling (stochastics, Technical U.

By (ii), we know that [xi] = [xi](x) is a

monotone function about x.

A

monotone function is obviously monotone-with-fixpoint, but the converse does not necessarily hold.

Of the calibration curves, 62-90% were best fit via the

MONOTONE function (lowest absolute SSRs), and 9-28% by MOD4P.

With LD, to get E(p) a strictly

monotone function requires a market supply function S(p) with [-S(p)] monotone.

If d[bar.w]/ds has no zero point, then [bar.w](s) is a

monotone function of s [member of] (-[infinity], +[infinity]); if d[bar.w]/ds has one zero point [s.sub.0] [member of] (-[infinity], +[infinity]), then [bar.w](s) is a

monotone function on both (-[infinity], [s.sub.0]] and [[s.sub.0], +[infinity]).

For example, a differentiable nowhere

monotone function (see, e.g., [2,5]).

Sung "A general purpose fuzzy controller for

monotone functions", IEEE Trans.

They cover Hardy's inequality and related topics, some weighted norm inequalities, the Hardy-Stecklov operator, higher order Hardy inequalities, fractional or Hardy inequalities, integral operators on the cone of

monotone functions, and new and complementary results.