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
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.