vol’terraning ikkinchi tur integral tenglamasi. terasiyalangan yadro. rezol’venta

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1662926015.doc ò + = x a x f dy y y x k x ) ( ) ( ) , ( ) ( j l j .... ), ( , ...... ), ( ), ( ), ( 2 1 0 x x x x n j j j j ò - + = x a n n dy y y x k x f x ) ( ) , ( ) ( ), ( 1 0 j l j j ) , ( max , ) ( max y x k n x f m = = , ) ( 0 m x £ j ,....., ) ( ) ( ) , ( ) ( ) ( 0 0 1 ò - £ = - x a a x mn y d y y x k x x l j l j j , .... , 2 , 1 , …

holda (3) tengsizlikga ega bo’lamiz. musbat hadli funksional qator parametrning ixtiyoriy chekli qiymatida tekis yaqinlashuvchi bo’lgani uchun (3) tengsizliklarga asosan (1) funksiyalar ketma – ketligi absolyut va tekis yaqinlashuvchi bo’lib, uning limiti bo’lgan funksiya (1) tenglamaning yechimidan iborat bo’ladi. endi (1) tenglam yechimining yagona ekanligini ko’rsatamiz. faraz qilaylik (1) tenglama ikkita va uzluksiz yechimlarga ega bo’lsin. bularning ayirmasi bir jinsli (4) tenglamani qanoatlantiradi. deb belgilab olsak, (4) dan darhol tengsizlik kelib chiqadi. bundan foydalanib (4) tenglikdan tengsizlikni hosil qilamiz. bu jarayonni davom ettirib, ixtiyoriy natural uchun tengsizlikni hosil qilamiz. bu tengsizlikdan da yoki ekanligi kelib chiqadi. shunday qilib quyidagi xulosaga keldik. vol’terraning ikkinchi tur (1) integral tenglamasi, uning yadrosi va ozod hadi uzluksiz fuksiyalar bo’lgabda parametrning har bir chekli qiymatida yagona yechimga ega bo’ladi. shu dalil bilan vol’terraning ikkinchi tur integral tenglamasi har bir uchun yechimga ega bo’lavermaydigan fredgolmning ikkinchi tur integral tenglamasidan tubdan farq qiladi. 2. iterasiyalangan yadro. tengsizlik …

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1662926015.doc ò + = x a x f dy y y x k x ) ( ) ( ) , ( ) ( j l j .... ), ( , ...... ), ( ), ( ), ( 2 1 0 x x x x n j j j j ò - + = x a n n dy y y x k x f x ) ( ) , ( ) ( ), ( 1 0 j l j j ) , ( max , ) ( max y x k n x f m = = , ) ( 0 m x £ j ,....., ) ( ) ( ) , ( ) ( ) ( 0 0 1 …

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