Tasɣnt tuɣnijt

Tasɣnt illan ɣ uẓlmaḍ tga tuɣnijt; ama talli illan ɣ ufasi tga taffnsut.

Ɣ tusnakt, ar nttini i kra n tasɣnt nɣ tawuri $f$ mas tga tuɣnijt iɣ tga tasɣnt tuzlt nns $-f$ tga taffnsut. Tga tasɣnt tuɣnijt yat tasɣnt nna dar illa wafa ɣ uflla d tnnurẓm ɣ izddar nns. Ar as nttini s tɛrabt Dalla Muqaɛɛara.

Asnml

Asnml amzwaru: Ar nttini i kra n tasɣnt nɣ tawuri

$f$

mas tga tuɣnijt iɣ tga tasɣnt tuzlt nns

$-f$

tga taffnsut.

Asnml ad irwas nit ɣwad ddaw-as

Asnml wis-sin: Ar nttini i kra n tasɣnt nɣ tawuri

$f$

n yan uzilal

$I$

itddan s ℝ mas tga tuɣnijt iɣ, i kraygat

$x_1$

d

$x_2$

illan ɣ

$I$

d kraygat

$t$

illan ɣ

$[0;1]$

, danrɣ:

$$f(t{x}_1+(1-t)x_2)\ge tf(x_1)+(1-t)f(x_2).$$

Amdya n tisɣunin ittwazlamn

Nṭṭaf sin tisflas:

Tasflst: Ad tg

$f$

yat tasɣnt ittwazlamn ɣ yan uzilal

$I$

.

• Tga $f$ tuɣnijt iɣ d ɣar iɣ illa udm n tasɣnt ddu kraygat yan zɣ iṭunjutin nns ;
• Tga $f$ tuɣnijt iɣ d ɣar iɣ ar itnusru azllum nns ɣ $I$.

Nẓḍar ad nsfɣ ɣilad tisflst tis-snat

• masd kullu tisɣunin lli ganin tuɣnijinin d ttwazlamn (ɣ kra n uzilal ilaw) hat gan n tasrkmt $C^1$ ;
• alkam ad, ar t nsxddam bzzaf bac ad nslkn bla amalad tuɣnijt nɣ takunkavit n kra n imdyatn bḍḍbt :

Alkam: Ad tg

$f$

yat tasɣnt ittwazlamn snat twal ɣ yan uzilal

$I$

. Tga

$f$

tuɣnijt iɣ d ɣar iɣ iga azllum nns wis-sin

$f^{″}$

ila s watign uzdirn nɣ igadda d amya.

Imdyatn n tisɣunin tuɣnijinin

Imdyatn n tisɣunin tuɣnijinin

Zɣ tisɣunin tuɣnijinin irxan, nẓḍar ad nbdr s usml ugmiḍn n tisɣunin taffnsunin ilawn, zund s umdya:

• $x\mapsto -x^n$ d $n$ tga ummid ayugan ;
• $x\mapsto exp(x)$.

Ad nbdr ula kra n tisɣunin timsuɣalin n tisɣunin taffnsunin, zund s umdya ɣ ℝ₊*:

• Tasɣnt n ulugaritm agaman
• Tasɣnt taẓḍurt $x\mapsto x^a$ iɣ $0\le a\le 1.$

S yat tɣarast igan tamatayt, tisɣunin ittwazlamn snat twal nna dar iga uzllum wis-sin uzdir bdda gan tisɣunin tuɣnijinin. Mac tasɣnt tuɣnijt macci ḍaṛuṛi ad tettwazlam ula nttat, xklli s nẓḍar ad nttannay ɣ tasɣnt ad n $x\mapsto \mid x\mid$.

Ẓṛ uggar

• Asaḍuf n id kusinus
• Targadda n Cauchy–Schwarz
• Alugaritm agaman
• Asktiɣmr

Amawal

Tiguriwin

• Tasɣnt = fonction
• Tuɣnijt = concave
• Tuzlt = oppose
• Taffnsut = convexe
• Azilal = intervalle
• Ittwazlamn = derivable
• Udm = courbe
• Azllum = derive
• Itnusru = decroit
• Ilaw = reel
• Amalad = mal
• Uzdir = negatif
• Ayugan = paire
• Ummid = entier
• Amsuɣal = reciproque

Imawaln

Amawal umniḍ DGLAi n Asinag Agldan n Tussna Tamaziɣt, s kraḍ tutlayin (tamaziɣt tatrart tamɣribit - tafransist - taɛrabt) [Alink nns]

Amawal Tafsut n tusnakt - MCB Alger, Tiwi Uzzu s sin tutlayin (tamaziɣt taqbaylit - tafransist) [Alink nns] Talɣa:Aggur:Tusnakt/Tin imgradn