chiziqli funkstionallar

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1445917853_61961.doc k e f ® : k x f x f e y x y f x f y x f î = î + = + l l l ) ( ) ( , ) ( ) ( ) ( f r k = k e f ® : 0 > e e î 0 x 0 x u u x î x e e 0 x u e e 0 0 ) ( ) ( x f x f e - > ) ( ) ( 1 0 0 x f x f e - > z x f x = ) ( 0 0 1 ) ( = z f h z î e e - < < - f z ёки z f 1 1 ) ( f d ва f z z f d 1 1 inf 1 ) ( £ - < = = …

$nuqtaning atrofidagi mavjudki, munosabat bajariladi. demak, to’plam u nuqtaning atrofi bo’ladi. agar bo’lsa, bajariladi. demak, to’plam u nuqtaning izlanayotgan atrofi bo’ladi, ya’ni funkstional u nuqtada uzluksizdir. u nuqtaning ixtiyoriy ekanligidan funkstionalning e fazoda uzluksizligini hosil qilamiz. chiziqli funkstional bo’lib, biror element uchun bo’lsin. u holda to’plam e ning qism fazosi bo’ladi. haqiqatdan ham, agar bo’lsa, ekanligi kelib chiqadi. chiziqli funkstional orqali qurilgan to’plamni funkstionalning yadrosi deyiladi va u ga tegishli har qanday vektorni yagona tarzda ko’rinishda ifodalash mumkin. haqiqatdan ham, bo’lsin. u holda vektor n ga tegishli bo’ladi, chunki . demak, ixtiyoriy vektorni ko’rinishda yozish mumkin. (2) yoyilmaning yagonaligini ham ko’rsatish mumkin, chunki x elementini yana boshqa usulda ko’rinishda yozish mumkin bo’lsa, bundan tenglikni hosil qilamiz. ekanligini e’tiborga olib, tengliklarga ega bo’lamiz. demak, u har qanday vektorni faqat bir usulda shaklda yozish mumkin, ya’ni e fazo va n qism fazolarning to’g’ri yig’indisidan iborat. demak, bundan e\n faktor fazoning o’lchovi 1 …$

mumkinki funkstionalning normasi uchun qo’yidagi tenglik o’rinli to’plam bilan ( orasidagi masofa, ya’ni . haqiqatdan ham to’plamning har qanday elementi x uchun munosabat o’rinli, ya’ni bajariladi. agar deb belgilash kiritsak, tengsizlik kelib chiqadi. funkstional normasining ta’rifiga asosan ixtiyoriy son uchun shunday x0 element mavjudki bajariladi. bundan kelib chiqadi. agar deb belgilasak, bo’lib, o’rinlidir. shuning uchun bajariladi. bu erda e ning ixtiyoriy ekanligin e’tiborga olib, tengsizlikni hosil qilasi z. demak, bo’ladi. misollar. 1. s fazoda berilgan tenglik bilan aniqlangan funkstional chiziqli bo’ladi. haqiqatdan ham, tengliklar bajarilaji. 2. normalangan s[0,1] fazoda berilgan ushbu funkstional ham cheklidir. 3. s fazoda berilgan va ushbu tenglik bilan aniqlangan funkstional ham chiziqli bo’ladi. _1260177811.unknown _1260177885.unknown _1260177933.unknown _1260178023.unknown _1260178036.unknown _1260178056.unknown _1260178067.unknown _1260178079.unknown _1260178084.unknown _1260178073.unknown _1260178063.unknown _1260178042.unknown _1260178025.unknown _1260178026.unknown _1260178024.unknown _1260178019.unknown _1260178021.unknown _1260178022.unknown _1260178020.unknown _1260178017.unknown _1260178018.unknown _1260177941.unknown _1260178016.unknown _1260177905.unknown _1260177922.unknown _1260177927.unknown _1260177912.unknown _1260177893.unknown _1260177900.unknown _1260177889.unknown _1260177848.unknown _1260177867.unknown _1260177876.unknown _1260177880.unknown _1260177872.unknown _1260177859.unknown _1260177863.unknown _1260177852.unknown _1260177831.unknown _1260177840.unknown _1260177843.unknown _1260177835.unknown _1260177824.unknown …

nown _1260177702.unknown _1260177679.unknown _1260177426.unknown _1260177489.unknown _1260177643.unknown _1260177650.unknown _1260177524.unknown _1260177621.unknown _1260177506.unknown _1260177434.unknown _1260177465.unknown _1260177469.unknown _1260177473.unknown _1260177457.unknown _1260177430.unknown _1244441066.unknown _1244442009.unknown _1244444891.unknown _1244446408.unknown _1260177400.unknown _1260177416.unknown _1244446513.unknown _1244448094.unknown _1244446258.unknown _1244446308.unknown _1244445703.unknown _1244442509.unknown _1244442556.unknown _1244442413.unknown _1244441595.unknown _1244441668.unknown _1244441493.unknown _1243949773.unknown _1243949910.unknown _1244440775.unknown _1243949795.unknown _1243949691.unknown _1243949212.unknown _1243949497.unknown

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1445917853_61961.doc k e f ® : k x f x f e y x y f x f y x f î = î + = + l l l ) ( ) ( , ) ( ) ( ) ( f r k = k e f ® : 0 > e e î 0 x 0 x u u x î x e e 0 x u e e 0 0 ) ( ) ( x f x f e - > ) ( ) ( 1 0 0 x f x f e - > z x f x = ) ( 0 0 1 ) ( = z f h z î e e - < …

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