# kumer funktsioon

olemus
reaalvuline funktsioon $$f$$, mille korral
$$f (ax + bx' ) \le a f (x ) + b f (x' )$$,
kus
$$x$$ ja $$y$$ on reaalarvud
$$a$$ ja $$b$$ on positiivsed reaalarvud,
mille summa $$a + b = 1$$
=
a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval

näide
ruutfunktsioon $$f(x) = x^2$$

ülevaateid
http://mathworld.wolfram.com/ConvexFunction.html

https://en.wikipedia.org/wiki/Convex_function

https://web.stanford.edu/class/ee364a/lectures/functions.pdf

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_real_variable)

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_complex_variable)

https://www.princeton.edu/~aaa/Public/Teaching/ORF523/S16/ORF523_S16_Lec7_gh.pdf

vt ka
- kumer
- kumer hulk

# kumer funktsioon

olemus
reaalvuline funktsioon $$f$$, mille korral
$$f (ax + bx' ) \le a f (x ) + b f (x' )$$,
kus
$$x$$ ja $$y$$ on reaalarvud
$$a$$ ja $$b$$ on positiivsed reaalarvud,
mille summa $$a + b = 1$$
=
a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval

näide
ruutfunktsioon $$f(x) = x^2$$

ülevaateid
http://mathworld.wolfram.com/ConvexFunction.html

https://en.wikipedia.org/wiki/Convex_function

https://web.stanford.edu/class/ee364a/lectures/functions.pdf

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_real_variable)

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_complex_variable)

https://www.princeton.edu/~aaa/Public/Teaching/ORF523/S16/ORF523_S16_Lec7_gh.pdf

vt ka
- kumer
- kumer hulk

Palun oodake...

# kumer funktsioon

olemus
reaalvuline funktsioon $$f$$, mille korral
$$f (ax + bx' ) \le a f (x ) + b f (x' )$$,
kus
$$x$$ ja $$y$$ on reaalarvud
$$a$$ ja $$b$$ on positiivsed reaalarvud,
mille summa $$a + b = 1$$
=
a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval

näide
ruutfunktsioon $$f(x) = x^2$$

ülevaateid
http://mathworld.wolfram.com/ConvexFunction.html

https://en.wikipedia.org/wiki/Convex_function

https://web.stanford.edu/class/ee364a/lectures/functions.pdf

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_real_variable)

https://www.encyclopediaofmath.org/index.php/Convex_function_(of_a_complex_variable)

https://www.princeton.edu/~aaa/Public/Teaching/ORF523/S16/ORF523_S16_Lec7_gh.pdf

vt ka
- kumer
- kumer hulk

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Vabandame!