Nuprl Definition : convex-on
convex-on(I;x.f[x]) ==
∀x,y,t:ℝ. ((x ∈ I)
⇒ (y ∈ I)
⇒ (t ∈ [r0, r1])
⇒ (f[(t * x) + ((r1 - t) * y)] ≤ ((t * f[x]) + ((r1 - t) * f[y]))))
Definitions occuring in Statement :
rccint: [l, u]
,
i-member: r ∈ I
,
rleq: x ≤ y
,
rsub: x - y
,
rmul: a * b
,
radd: a + b
,
int-to-real: r(n)
,
real: ℝ
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
natural_number: $n
Definitions occuring in definition :
all: ∀x:A. B[x]
,
real: ℝ
,
implies: P
⇒ Q
,
i-member: r ∈ I
,
rccint: [l, u]
,
rleq: x ≤ y
,
radd: a + b
,
rmul: a * b
,
rsub: x - y
,
int-to-real: r(n)
,
natural_number: $n
FDL editor aliases :
convex-on
Latex:
convex-on(I;x.f[x]) ==
\mforall{}x,y,t:\mBbbR{}.
((x \mmember{} I)
{}\mRightarrow{} (y \mmember{} I)
{}\mRightarrow{} (t \mmember{} [r0, r1])
{}\mRightarrow{} (f[(t * x) + ((r1 - t) * y)] \mleq{} ((t * f[x]) + ((r1 - t) * f[y]))))
Date html generated:
2018_05_22-PM-02_19_01
Last ObjectModification:
2017_10_20-PM-01_13_35
Theory : reals
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