Last Updated：2025/12/03
(mathematical analysis) A property which can be said to be held by some point in the domain of a real-valued function if there exists a neighborhood of that point and a certain constant such that for any other point in that neighborhood, the absolute value of the difference of their function values is less than the product of the constant and the absolute value of the difference between the two points.
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Lipschitz condition
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Source Word
Lipschitz condition
Noun
(mathematical
analysis)
A
property
which
can
be
said
to
be
held
by
some
point
in
the
domain
of
a
real-valued
function
if
there
exists
a
neighborhood
of
that
point
and
a
certain
constant
such
that
for
any
other
point
in
that
neighborhood,
the
absolute
value
of
the
difference
of
their
function
values
is
less
than
the
product
of
the
constant
and
the
absolute
value
of
the
difference
between
the
two
points.
Japanese Meaning
数学的解析における概念で、ある実数値関数が、特定の点の近傍内で、任意の2点間においてその関数値の差が、ある一定の正の定数と入力値の差の積よりも小さいという性質。すなわち、ある定数 L > 0 と、その点の近傍が存在し、任意の x, y に対して |f(x) - f(y)| ≤ L|x - y| が成立することを指す。
Sense（1）
(mathematical
analysis)
A
property
which
can
be
said
to
be
held
by
some
point
in
the
domain
of
a
real-valued
function
if
there
exists
a
neighborhood
of
that
point
and
a
certain
constant
such
that
for
any
other
point
in
that
neighborhood,
the
absolute
value
of
the
difference
of
their
function
values
is
less
than
the
product
of
the
constant
and
the
absolute
value
of
the
difference
between
the
two
points.
（ plural ）
