ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC SƯ PHẠM ĐÀM THỊ HỒNG NGUN LÝ BÀI TỐN PHỤ HIỆU CHỈNH TÌM ĐIỂM BẤT ĐỘNG CHUNG CHO MỘT HỌ VÔ HẠN ÁNH XẠ GIẢ CO CHẶT LUẬN VĂN THẠC SĨ TOÁN HỌC THÁI NGUYÊN - 2016 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC SƯ PHẠM ĐÀM THỊ HỒNG NGUYÊN LÝ BÀI TOÁN PHỤ HIỆU CHỈNH TÌM ĐIỂM BẤT ĐỘNG CHUNG CHO MỘT HỌ VƠ HẠN ÁNH XẠ GIẢ CO CHẶT Chuyên ngành: TOÁN GIẢI TÍCH Mã số: 60.46.01.02 LUẬN VĂN THẠC SĨ TỐN HỌC Người hướng dẫn khoa học: TS LÂM THÙY DƯƠNG THÁI NGUYÊN - 2016 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✶ ▼ô❝ ❧ô❝ ▲ê✐ ❝❛♠ ➤♦❛♥ ✐ ▲ê✐ ❝➯♠ ➡♥ ✐✐ ▼ơ❝ ❧ơ❝ ✐✐✐ ▼ét sè ❦ý ❤✐Ư✉ ✈➭ ✈✐Õt t➽t ✐✈ ▼ë ➤➬✉ ✶ ✶ ❑✐Õ♥ t❤ø❝ ❝❤✉➮♥ ❜Þ ✹ ✶✳✶✳ ▼ét sè ❦❤➳✐ ♥✐Ư♠ ❝đ❛ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✶✳✶✳ ➜Þ♥❤ ♥❣❤Ü❛ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹ ✶✳✶✳✷✳ ▼ét sè ❦❤➳✐ ♥✐Ö♠ ❧✐➟♥ q✉❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✷✳ ❇➭✐ t♦➳♥ ➤✐Ó♠ ❜✃t ➤é♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✶✳✸✳ ❇➭✐ t♦➳♥ ➤➷t ❦❤➠♥❣ ❝❤Ø♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✸✳✶✳ ❑❤➳✐ ♥✐Ư♠ ✈Ị ❜➭✐ t♦➳♥ ❝❤Ø♥❤ ✈➭ ❦❤➠♥❣ ❝❤Ø♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✸✳✷✳ ❈➳❝ ♣❤➢➡♥❣ ♣❤➳♣ ❤✐Ö✉ ❝❤Ø♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✶✳✹✳ ◆❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ ❝❤♦ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ✶✼ ✶✳✹✳✶✳ ❇➭✐ t♦➳♥ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✶✳✹✳✷✳ P❤➢➡♥❣ ♣❤➳♣ ❜➭✐ t♦➳♥ ♣❤ô ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✹✳✸✳ ❚❤✉❐t t♦➳♥ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ ❝❤♦ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷ ◆❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ô ❤✐Ư✉ ❝❤Ø♥❤ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t ✷✽ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✷✳✶✳ P❤➢➡♥❣ ♣❤➳♣ ❤✐Ư✉ ❝❤Ø♥❤ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✷✳ ◆❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t ❑Õt ❧✉❐♥ ❚➭✐ ❧✐Ö✉ t❤❛♠ ❦❤➯♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✸ ✹✹ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐ ❧ê✐ ❝❛♠ ➤♦❛♥ ❚➠✐ ①✐♥ ❝❛♠ ➤♦❛♥ r➺♥❣ ♥é✐ ❞✉♥❣ tr×♥❤ ❜➭② tr♦♥❣ ❧✉❐♥ ✈➝♥ ♥➭② ❧➭ tr✉♥❣ t❤ù❝✱ ❦❤➠♥❣ trï♥❣ ❧➷♣ ✈í✐ ❝➳❝ ➤Ị t➭✐ ❦❤➳❝ ✈➭ ❝➳❝ t➭✐ ❧✐Ö✉ trÝ❝❤ ❞➱♥ tr♦♥❣ ❧✉❐♥ ✈➝♥ ➤➲ ợ ỉ rõ ố ị LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✐ ❧ê✐ ❝➯♠ ➡♥ ▲✉❐♥ ✈➝♥ ♥➭② ➤➢ỵ❝ ❤♦➭♥ t❤➭♥❤ t➵✐ ❚r➢ê♥❣ ➜➵✐ ❤ä❝ ❙➢ ♣❤➵♠ t❤✉é❝ ➜➵✐ ❤ä❝ ❚❤➳✐ ◆❣✉②➟♥ ❞➢í✐ sù ❤➢í♥❣ ❞➱♥ ❝đ❛ ❚❙✳ ▲➞♠ ❚❤ï② ❉➢➡♥❣✳ ❚➳❝ ❣✐➯ ①✐♥ ❜➭② tá ❧ß♥❣ ❜✐Õt ➡♥ s➞✉ s➽❝ ♥❤✃t tí✐ ỉ t tì ữ ý ❦✐Õ♥ ➤ã♥❣ ❣ã♣ q✉Ý ❜➳✉ tr♦♥❣ s✉èt q✉➳ tr×♥❤ ❤ä❝ t❐♣ ✈➭ ♥❣❤✐➟♥ ❝ø✉✳ ❚➳❝ ❣✐➯ ①✐♥ ❝❤➞♥ t❤➭♥❤ ❝➯♠ ➡♥ tí✐ ❇❛♥ ●✐➳♠ ❤✐Ư✉ ❚r➢ê♥❣ ➜➵✐ ❤ä❝ ❙➢ ♣❤➵♠✱ P❤ß♥❣ s❛✉ ➤➵✐ ❤ä❝ ✈➭ ❇❛♥ ❈❤đ ♥❤✐Ư♠ ❦❤♦❛ ❚♦➳♥ ❚r➢ê♥❣ ➜➵✐ ❤ä❝ ❙➢ ♣❤➵♠ ✲ ➜➵✐ ❤♦❝ ❚❤➳✐ ◆❣✉②➟♥ ➤➲ t➵♦ ♠ä✐ ➤✐Ị✉ ❦✐Ư♥ t❤✉❐♥ ❧ỵ✐ ❝❤♦ t➳❝ ❣✐➯ tr♦♥❣ s✉èt t❤ê✐ ❣✐❛♥ ❧➭♠ ❧✉❐♥ ✈➝♥✳ ❚➳❝ ❣✐➯ ①✐♥ ❝❤➞♥ t❤➭♥❤ ❝➯♠ ➡♥ tí✐ ❝➳❝ ❛♥❤✱ ❝❤Þ ❡♠ ❤ä❝ ✈✐➟♥ ❑✷✷ ➤➲ tr❛♦ ➤ỉ✐✱ ➤é♥❣ ✈✐➟♥ ✈➭ ❦❤Ý❝❤ ❧Ư t➳❝ ❣✐➯ tr♦♥❣ q✉➳ tr×♥❤ ❤ä❝ t❐♣✱ ♥❣❤✐➟♥ ❝ø✉ ✈➭ ❧➭♠ ❧✉❐♥ ✈➝♥✳ ❚➳❝ ❣✐➯ ①✐♥ ❦Ý♥❤ t➷♥❣ ♥❤÷♥❣ ♥❣➢ê✐ t❤➞♥ ②➟✉ tr♦♥❣ ❣✐❛ ➤×♥❤ ❝đ❛ ♠×♥❤ ♥✐Ị♠ ✈✐♥❤ ❤➵♥❤ ♥➭②✳ ❚➳❝ ❣✐➯ ➜➭♠ ❚❤Þ ❍å♥❣ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✐✐ ▼ô❝ ❧ô❝ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✈ ▼ét sè ❦ý ❤✐Ö✉ ✈➭ ✈✐Õt t➽t H ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt t❤ù❝ E ❦❤➠♥❣ ❣✐❛♥ ❇❛♥❛❝❤ t❤ù❝ , tÝ❝❤ ✈➠ ❤➢í♥❣ tr➟♥ ❍ ❝❤✉➮♥ tr➟♥ H D(A) ♠✐Ị♥ ①➳❝ ➤Þ♥❤ ❝đ❛ ➳♥❤ ①➵ N t❐♣ ❤ỵ♣ ❝➳❝ sè tù ♥❤✐➟♥ R t❐♣ ❤ỵ♣ ❝➳❝ sè t❤ù❝ I t♦➳♥ tư ➤å♥❣ ♥❤✃t ∅ t rỗ x ọ xn x0 {xn } ❤é✐ tơ ♠➵♥❤ ✈Ị x0 xn ❞➲② {xn } ❤é✐ tơ ②Õ✉ ✈Ị x0 x0 A x LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✶ ▼ë ➤➬✉ ❇➭✐ t♦➳♥ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝đ❛ ♠ét ➳♥❤ ①➵ T ❧➭ ❜➭✐ t♦➳♥ ❝ã ♥❤✐Ị✉ ø♥❣ ❞ơ♥❣ tr♦♥❣ ❣✐➯✐ tÝ❝❤✱ ♥❤✃t ❧➭ tr♦♥❣ ❧ý t❤✉②Õt ❝➳❝ ♣❤➢➡♥❣ tr×♥❤✳ ❚r♦♥❣ ♥❤✐Ị✉ trờ ợ ệ ột trì ợ q ề ✈✐Ư❝ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝đ❛ ♠ét ➳♥❤ ①➵ t❤Ý❝❤ ❤ỵ♣✳ ❈❤➻♥❣ ❤➵♥ ♥❤➢✱ ❝❤♦ ➳♥❤ ①➵ tr♦♥❣ f (x) = y X✱ y X ❧➭ ♠ét ❦❤➠♥❣ ❣✐❛♥ t✉②Õ♥ tÝ♥❤✱ ❧➭ ♠ét ♣❤➬♥ tư ❝è ➤Þ♥❤ ❝đ❛ ❧➭ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝đ❛ ➳♥❤ ①➵ F X f ❧➭ t❤× ệ ủ trì ị F (x) = x + f (x) y ữ ị ý ➤✐Ĩ♠ ❜✃t ➤é♥❣ ♥ỉ✐ t✐Õ♥❣ ➤➲ ①✉✃t ❤✐Ư♥ tõ ➤➬✉ t❤Õ ❦û ❳❳✱ tr♦♥❣ ➤ã ♣❤➯✐ ❦Ó ➤Õ♥✿ ✬✬ ◆❣✉②➟♥ ❧ý ➤✐Ó♠ ❜✃t ➤é♥❣ ❇r♦✉❞❡r ✭✶✾✶✷✮✬✬✱ ✬✬ ◆❣✉②➟♥ ❧ý ➳♥❤ ①➵ ❝♦ ❇❛♥♥❛❝❤ ✭✶✾✷✷✮✬✬ ✈➭ ❝➳❝ ❦Õt q✉➯ ❦✐♥❤ ➤✐Ó♥ ♥➭② ➤➲ ➤➢ỵ❝ ♠ë ré♥❣ r❛ ❧í♣ ❝➳❝ ➳♥❤ ①➵ ữ ị ý ✈Ị ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❦❤➠♥❣ ❝❤Ø ❝ã ø♥❣ ❞ơ♥❣ tr♦♥❣ t♦➳♥ ❤ä❝ ♠➭ ❝ß♥ ❝ã ♥❤✐Ị✉ ø♥❣ ❞ơ♥❣ tr♦♥❣ ❝➳❝ ❧Ü♥❤ ✈ù❝ ❦❤➳❝✱ ♥❤➢ ❧➭✿ ①ư ❧ý tÝ♥ ❤✐Ư✉✱ ①ư ❧ý ➯♥❤✱✳✳✳ ❉♦ ➤ã✱ ❜➭✐ t♦➳♥ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❧➭ ♠ét ✈✃♥ ➤Ị ➤➢ỵ❝ sù q✉❛♥ t➞♠ ❝đ❛ ♥❤✐Ị✉ ♥❤➭ t♦➳♥ ❤ä❝✳ ▼ơ❝ ➤Ý❝❤ ❝đ❛ ❧✉❐♥ ✈➝♥ ❧➭ ♥❣❤✐➟♥ ❝ø✉ ♣❤➢➡♥❣ ♣❤➳♣ ❤✐Ư✉ ❝❤Ø♥❤ ◆❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ➤Ĩ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ❝➳❝ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t✱ tr➢ê♥❣ ❤ỵ♣ r✐➟♥❣ ❧➭ ♠ét ❤ä ➳♥❤ ①➵ ❦❤➠♥❣ ❣✐➲♥✱ tr♦♥❣ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt✳ ❑❤➳✐ ♥✐Ư♠ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t ➤➢ỵ❝ ❝➳❝ ♥❤➭ t♦➳♥ ❤ä❝ ❋✳ ❊✳ ❇r♦✉❞❡r ✈➭ ❲✳ ❱✳ P❡tr②s❤②♥ [✺] ➤➢❛ r❛ ♥➝♠ ✶✾✻✼✳ ❍ä ➤➲ ➤Þ♥❤ ♥❣❤Ü❛ r➺♥❣✱ ♠ét ➳♥❤ ①➵ ➤Þ♥❤ tr➟♥ ♠ét t❐♣ ❧å✐ ➤ã♥❣ C ❝đ❛ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt H ❧➭ T ①➳❝ λ ✲ ❣✐➯ ❝♦ ❝❤➷t ♥Õ✉ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ➳♥❤ ①➵ T T (x) − T (y) ✈í✐ ✷ t❤á❛ ♠➲♥✿ ≤ λ < 1✳ ≤ x−y +λ ❚r♦♥❣ tr➢ê♥❣ ❤ỵ♣ ❦❤✐ (I − T )(x) − (I − T )(y) λ = t❤× ➳♥❤ ①➵ ✲ ❣✐➯ ❝♦ ❝❤➷t ❧➭ ♠ét ➳♥❤ ①➵ ❦❤➠♥❣ ❣✐➲♥✳ C ❈❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ λi ✲ ❣✐➯ ❝♦ ❝❤➷t✱ {Ti }∞ i=1 tõ ♠ét t❐♣ ❧å✐ ➤ã♥❣ ❝ñ❛ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt H ✱ s❛♦ ❝❤♦ F = H ✈➭♦ ∞ i=1 F ix (Ti ) = φ✱ ë ➤➞② F ix (Ti ) ❧➭ t❐♣ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝đ❛ ➳♥❤ ①➵ Ti ✳ ❳Ðt ❜➭✐ t♦➳♥✿ ❚×♠ u∗ ∈ F P❤➢➡♥❣ ♣❤➳♣ ❜➭✐ t♦➳♥ ♣❤ơ ➤➢ỵ❝ ➤Ị ①✉✃t ❜ë✐ ❈♦❤❡♥ [✼] ✈➭♦ ♥➝♠ ✶✾✽✵ ❦❤✐ ♥❣❤✐➟♥ ❝ø✉ ❜➭✐ t♦➳♥ tè✐ ➢✉✳ ◆➝♠ ✶✾✽✽✱ ❈♦❤❡♥ [✽] ✈❐♥ ❞ô♥❣ ♣❤➢➡♥❣ ♣❤➳♣ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ➤Ĩ t×♠ ♥❣❤✐Ư♠ ❝❤♦ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ❝ỉ ➤✐Ĩ♥✿ ❚×♠ u∗ ∈ C s❛♦ ❝❤♦ F (u∗ ) , v − u∗ ≥ v ∈ C, ✈í✐ F : C→H ✭✵✳✶✮ ❧➭ ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈➭ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③✳ ➜è✐ ✈í✐ ♣❤➢➡♥❣ ♣❤➳♣ ❜➭✐ t♦➳♥ ♣❤ơ ➤ß✐ ❤á✐ ➳♥❤ ①➵ ♠➵♥❤✳ ❱❐② ❦❤✐ ➳♥❤ ①➵ F F ❝ã tÝ♥❤ ❝❤✃t ➤➡♥ ➤✐Ö✉ ❝❤Ø ❝ã tÝ♥❤ ❝❤✃t ➤➡♥ ➤✐Ư✉ t❤× ❝ã ❝➳❝❤ ♥➭♦ ➤Ĩ tì ệ t ợ ể q✉②Õt ✈✃♥ ➤Ò ♥➭②✱ ♥➝♠ ✷✵✵✵✱ ❏✳ ❇❛❛s❛♥s✉r❡♥ ✈➭ ❆✳ ❆✳ ❑❤❛♥ [✹] ➤➲ ➤Ị ①✉✃t ♣❤➢➡♥❣ ♣❤➳♣ ♠í✐✱ ❧➭ ết ợ ữ ệ ỉ rr ♣❤➢➡♥❣ ♣❤➳♣ ❜➭✐ t♦➳♥ ♣❤ơ ✈➭ ❣ä✐ ❧➭✿ ✳ ❱í✐ ♣❤➢➡♥❣ ♣❤➳♣ ✬✬P❤➢➡♥❣ ♣❤➳♣ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤✬✬ ♥➭②✱ t❤❛② ❝❤♦ ✈✐Ư❝ ①➳❝ ➤Þ♥❤ ❝❤Ý♥❤ ①➳❝ ♥❣❤✐Ư♠ u∗ ❝đ❛ ❜➭✐ t♦➳♥ ✭✵✳✶✮✱ ❤ä ①➳❝ ➤Þ♥❤ ❞➲② ♥❣❤✐Ư♠ ①✃♣ ①Ø {zn }n≥0 ❝ñ❛ ❝➳❝ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ➤➲ ❝❤Ø♥❤ ❤ã❛ ✈➭ ❝❤ø♥❣ ♠✐♥❤ sù ❤é✐ tô ♠➵♥❤ ❝đ❛ ❞➲② ♥❣❤✐Ư♠ {zn }n≥0 tí✐ ♥❣❤✐Ư♠ u∗ ❝đ❛ ❜➭✐ t♦➳♥ ✭✵✳✶✮✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✈➭ t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ (A)✳ ✸✶ ❈❤♦ r > ✈➭ x ∈ H tï② ý✱ ➳♥❤ ①➵ Tr : H → C ①➳❝ ➤Þ♥❤ ♥❤➢ s❛✉✿ Tr (x) = {z ∈ K : G(z, v) + z − x, v − z ≥ ∀ v ∈ C} r ❑❤✐ ➤ã✱ t❛ ❝ã✿ (i) Tr ❧➭ ➳♥❤ ①➵ ➤➡♥ trÞ❀ (ii) Tr ❧➭ ➳♥❤ ①➵ ❦❤➠♥❣ ❣✐➲♥✱ tø❝ ❧➭ ✈í✐ Tr (x) − Tr (y) x✱ y ∈ H t❛ ❝ã✿ ≤ Tr (x) − Tr (y), x − y ; (iii) F ix(Tr ) = EP (G)❀ ë ➤➞②✱ EP (G) ❧➭ t❐♣ ➤✐Ó♠ ♥❣❤✐Ư♠ ❝đ❛ ❜➭✐ t♦➳♥ ❝➞♥ ❜➺♥❣ ✭✷✳✼✮✳ (iv) EP (G) ❧➭ ♠ét t❐♣ ❧å✐ ✈➭ ➤ã♥❣✳ ❇ỉ ➤Ị ✷✳✸ ✭❳❡♠ ❬✶✹❪✮ ❣✐❛♥ ❍✐❧❜❡rt ❈❤♦ ❧➭ ♠ét t❐♣ ❝♦♥ ❧å✐ ➤ã♥❣ rỗ ủ H sử T : C −→ H ❧➭ ➳♥❤ ①➵ ❞❡♠✐❝❧♦s❡❞ t➵✐ ❞➲② C ❧➭ ➳♥❤ ①➵ λ ✲ ❣✐➯ ❝♦ ❝❤➷t✳ ❑❤✐ ➤ã✱ I − T 0❀ tø❝ ❧➭✱ ❞➲② {xn } tr♦♥❣ C ❤é✐ tơ ②Õ✉ tí✐ x∈C ✈➭ {(I − T )(xn )} ❤é✐ tơ ♠➵♥❤ tí✐ 0✱ t❤× s✉② r❛ (I − T )(x) = 0✳ ❇ỉ ➤Ị ✷✳✹ ✭❳❡♠ ❬✶✶❪✮ ❣✐❛♥ ❍✐❧❜❡rt H✳ ❈❤♦ ●✐➯ sö C ❧➭ ♠ét t ó rỗ ủ T : C −→ H ➳♥❤ ①➵ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③✱ ✈í✐ ❤➺♥❣ sè ❇ỉ ➤Ị ✷✳✺ ✭❳❡♠ ❬✶✶❪✮ ❈❤♦ C ❧➭ ➳♥❤ ①➵ L= λ✲❣✐➯ ❝♦ ❝❤➷t✳ ❑❤✐ ➤ã✱ T ❧➭ 1+λ ột t ó rỗ ❝ñ❛ ❦❤➠♥❣ λ✲❣✐➯ ❝♦ ❝❤➷t✳ ❑❤✐ ➤ã✱ I − T 1−λ ❀ tø❝ ❧➭✱ ∀ x, y ∈ C t❛ ❝ã✿ ❧➭ ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈í✐ ❤➺♥❣ sè λ = 1−λ A(x) − A(y), x − y ≥ A(x) − A(y) ; ❣✐❛♥ ❍✐❧❜❡rt ë ➤➞②✱ H ✳ ●✐➯ sö T : C −→ H ❧➭ ➳♥❤ ①➵ A = I − T✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✷ ➜Þ♥❤ ❧ý s❛✉ ➤➞② ❧➭ ❦Õt q✉➯ ❝❤♦ sù tå♥ t➵✐ ♥❣❤✐Ö♠ ❤✐Ö✉ ❝❤Ø♥❤ ❝đ❛ ❜➭✐ t♦➳♥ ✭✷✳✺✮ ✈➭ tÝ♥❤ ❤é✐ tơ ♠➵♥❤ tí✐ ♥❣❤✐Ư♠ ➜Þ♥❤ ❧Ý ✷✳✶ ✭❳❡♠ ❬✻❪✮ ❣✐❛♥ ❍✐❧❜❡rt ✈➭♦ H H s❛♦ ❝❤♦ ✈➭ ❈❤♦ {Ti }∞ i=1 F = C ❝ñ❛ ❜➭✐ t♦➳♥ ✭✷✳✹✮✳ ❧➭ ♠ét t❐♣ ❝♦♥ ó rỗ ủ ột ọ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ ∞ i=1 F ix(Ti ) t❤ù❝ t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ u∗ ✭✷✳✻✮✳ = ∅✳ ●✐➯ sư r➺♥❣ λi ✲ ❣✐➯ ❝♦ ❝❤➷t tõ {γi }∞ i=1 C ❧➭ ♠ét ❞➲② sè ❑❤✐ ➤ã✱ t❛ ❝ã✿ (i) ỗ > t ó ♥❤✃t ♠ét ♥❣❤✐Ö♠ uα ❀ (ii) limα→0 uα = u∗ ✱ u∗ ∈ F ✱ u∗ ≤ y ∀ y ∈ F ❀ α−β ∗ (iii) uα − uβ ≤ u ✳ α ❈❤ø♥❣ ♠✐♥❤✳ (i) ●ä✐ y ❧➭ ➤✐Ó♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝ñ❛ ❤ä ❝➳❝ ➳♥❤ ①➵ λi ✲ ❣✐➯ ❝♦ ❝❤➷t {Ti }∞ i=1 ✳ ❑❤✐ ➤ã✱ ✈í✐ x∈C t❛ ❝ã✿ γi Ai (x) = γi Ai (x) − Ai (y) + Ai (y) ✭✷✳✽✮ ≤ γi Ai (x) − Ai (y) + γi Ai (y) ; ë ➤➞②✱ ❱× Ai = I − Ti ✳ y∈F ♥➟♥ Ti (y) = y ✱ ❤❛② Ai (y) = 0✳ ❚❤❡♦ ❇ỉ ➤Ị 2.5✱ A ❧➭ ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ♥➟♥ γi x−y = x−y − λi λi ∞ γi ❚❤❡♦ ➤✐Ị✉ ❦✐Ư♥ ✭✷✳✻✮✱ = γ < ∞✱ ♥➟♥ s✉② r❛ ➳♥❤ ①➵ B ✱ i=1 λi ∞ ♥❣❤Ü❛ ❜ë✐ B(x) = i=1 γi Ai (x)✱ ộ tụ tệt ố ỗ x C i Ai (x) i t ì ỗ Ai ợ ị ệ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③ ♥➟♥ ❝ị♥❣ ❧➭ ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ✈➭ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③ ✈í✐ ❤➺♥❣ sè B LB = γ ✳ ➜➷t Gi (u, v) = γi Ai (u), v − u , i ≥ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✸ ❚õ ✭✷✳✺✮ t❛ ❝ã✿ ∞ γi Ai (uα ), v − uα + α uα , v − uα ≥ ∀ v ∈ C i=1 ❚❛ ❧➵✐ ➤➷t ∞ Gi (u, v) = B(u), v − u G(u, v) = i=1 ✈➭ Gα (u, v) = G(u, v) + α u, v − u ❑❤✐ ➤ã ❜➭✐ t♦➳♥ ✭✷✳✺✮ ❝ã ❞➵♥❣✿ ❚×♠ uα ∈ C s❛♦ ❝❤♦ Gα (uα , v) ≥ v C ỗ i ❤➭♠ Gi (u, v) t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ (A)✳ ❉♦ ➤ã✱ ❤➭♠ G(u, v) =α>0 ❝ị♥❣ t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ (A)✳ ❚❤❡♦ ❇ỉ ➤Ị 2.1 ✈➭ ❇ỉ ➤Ị 2.2✱ ✈í✐ r ✈➭ x = 0✱ ❜➭✐ t♦➳♥ ✭✷✳✾✮ ❝ã ♥❣❤✐Ư♠ ❞✉② ♥❤✃t uα ✳ ➜✐Ị✉ ➤ã ❝❤ø♥❣ tá r➺♥❣ ỗ > t ó ệ ❞✉② ♥❤✃t uα ✳ (ii) ❚r➢í❝ ❤Õt ❝❤ó♥❣ t➠✐ ❝❤ø♥❣ ♠✐♥❤ r➺♥❣ uα ≤ y ❚❤❐t ✈❐②✱ ✈× y∈F ♥➟♥ ∀ y ∈ F Ai (y) = 0, i ≥ 1✳ ❉♦ ➤ã✱ B(uα ), y − uα + α uα , y − uα ≥ ∀ y ∈ F ◆❤➢♥❣ ➳♥❤ ①➵ Ai ✭✷✳✶✵✮ ✭✷✳✶✶✮ ❧➭ ➳♥❤ ①➵ ➤➡♥ ➤✐Ö✉ ♥➟♥ γi Ai (uα ), y − uα ≥ ∀ y ∈ F, i ≥ ❉♦ ➤ã uα , y − uα ≥ ∀ y ∈ F ❍❛② uα ≤ y ∀ y ∈ F LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚õ ➤ã s✉② r❛ ❞➲② {uα } ✸✹ ❜Þ ❝❤➷♥✳ ❑❤✐ ➤ã✱ tå♥ t➵✐ ♠ét ❞➲② ❝♦♥ {uαk } ❝ñ❛ ❞➲② {uα } ❤é✐ tơ ②Õ✉ tí✐ ♠ét ♣❤➬♥ tư u∗ ∈ C ✳ ❚✐Õ♣ t❤❡♦✱ t❛ ❝➬♥ ❝❤ø♥❣ ♠✐♥❤ ❚❤❐t ✈❐②✱ t❤❡♦ ❇ỉ ➤Ị λi = 2.5✱ t❤× u∗ ∈ F ✳ ❧➭ ❝➳❝ ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈í✐ ❤➺♥❣ sè Ai − λi ✱ tø❝ ❧➭ ∀ x, y ∈ C t❛ ❝ã✿ − λi Ai (x) − Ai (y) Ai (x) − Ai (y), x − y ≥ ❉♦ ➤ã✱ ✈í✐ ♠ét ❝❤Ø sè l ♥➭♦ ➤ã t❤× Al ✭✷✳✶✷✮ ❝ị♥❣ ❧➭ ♠ét ➳♥❤ ①➵ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈í✐ − λl ✳ ❍➡♥ ♥÷❛ Al (y) = 0✱ ♥➟♥ tõ ✭✷✳✶✷✮ s✉② r❛✿ − λl < γl Al (uαk ) ≤ γl Al (uαk ), uαk − y ❤➺♥❣ sè ∞ ≤ γi Ai (uαk ), uαk − y i=1 ✭✷✳✶✸✮ ≤ αk uαk , y − uαk ≤ αk y, y − uαk ≤ 2αk y −→ ❦❤✐ k → ∞ ❱❐② lim Al (uαk ) = k→∞ ❚❤❡♦ ❇ỉ ➤Ị 2.3✱ Al (u∗ ) = 0✱ s✉② r❛ ❇ỉ ➤Ị 2.2✱ ✈× F ix(Ti ) (i ❤❛② u∗ ∈ F ix(Tl )✳ ≥ 1) ❧➭ ❝➳❝ ❧❐♣ ❧å✐ ➤ã♥❣ ♥➟♥ F = ▼➷t ❦❤➳❝✱ ❧➵✐ t❤❡♦ ∞ i=1 F ix(Ti ) ❝ị♥❣ ❧➭ ♠ét t❐♣ ❧å✐ ➤ã♥❣✳ ▼➷t ❦❤➳❝✱ ♠ä✐ ➤✐Ĩ♠ tơ ②Õ✉ ➤Ị✉ ❧➭ ♥❣❤✐Ư♠ ❝ã ❝❤✉➮♥ ♥❤á ♥❤✃t✱ ❞♦ ✈❐② ❧➭ ❞✉② ♥❤✃t✳ ❉♦ ➤ã✱ ♠ä✐ ❞➲② ❝♦♥ s✉② r❛ ❞➲② uα ❝ị♥❣ ❤é✐ tơ ②Õ✉ tí✐ ❚r♦♥❣ ✭✷✳✶✵✮✱ t❛ t❤❛② ❣✐❛♥ ❍✐❧❜❡rt✱ t❛ ❝ã uα y ❜ë✐ u∗ u∗ ✈➭ {uαk } ❤é✐ tơ ②Õ✉ tí✐ u∗ ✳ ❚õ ➤ã u∗ ✱ ❦❤✐ α → 0✳ ✈➭ ✈❐♥ ❞ơ♥❣ tÝ♥❤ ❝❤✃t uα → u∗ t❤× s✉② r❛ E−S tr♦♥❣ ❦❤➠♥❣ uα − u∗ → ❦❤✐ α → 0✱ tø❝ ❧➭✿ lim uα = u∗ α→0 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com (iii) ✸✺ ❚❤❡♦ ✭✷✳✶✶✮ ✈➭ tÝ♥❤ ❝❤✃t ➤➡♥ ➤✐Ư✉ ❝đ❛ ➳♥❤ ①➵ B✱ ỗ , > t ó u , uβ − uα + β uβ , uα − uβ ≥ ⇔ β uβ , uα − uβ ≥ α uα , uβ − uα ⇔ β uβ , uα − uβ −α uβ , uα − uβ ≥ α uα , uβ − uα −α uβ , uα − uβ ⇔ (β − α) uβ , uα − uβ ≥ α uα − uβ |α − β| |α − β| ∗ ⇒ uα − uβ ≤ uβ ≤ u α α ✳ ❱❐② uα − uβ ≤ |α − β| ∗ u , α ✈í✐ α, > ị ý ợ ứ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ ❣✐➯ ❝♦ ❝❤➷t ❚r♦♥❣ ♠ơ❝ ♥➭② ❝❤ó♥❣ t➠✐ ①Ðt sù ❦Õt ợ ữ t ệ ỉ tt t ❜➭✐ t♦➳♥ ♣❤ơ ➤➲ tr×♥❤ ❜➭② tr♦♥❣ ❈❤➢➡♥❣ ✶ ➤Ĩ t❤✉ ➤➢ỵ❝ t❤✉❐t t♦➳♥ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ s❛✉✿ ❈❤♦ ϕ : H → R ❧➭ ♠ét ♣❤✐Õ♠ ❤➭♠ ❧å✐ ❝❤Ý♥❤ t❤➢ê♥❣ ✈➭ ❦❤➯ ✈✐ ●➞t❡❛✉①✱ ✈í✐ ➤➵♦ ❤➭♠ ϕ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈➭ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③❀ { n }n≥0 ✱ {αn }n≥0 ❧➭ ❤❛✐ ❞➲② sè t❤ù❝ ❞➢➡♥❣ t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥✿ ➜✐Ị✉ ❦✐Ư♥ Ψ (i) < n (ii) (iii) ≤ 1❀ < αn+1 ≤ αn ≤ 1❀ αn → ❦❤✐ n → ∞❀ ∞ n=0 n αn = ∞❀ ∞ n=0 n < ∞❀ ∞ (αn − αn+1 ) < ∞✳ n=0 αn3 n LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚❛ ❧✃② tï② ý z0 min{ϕ(z) + z∈C tr♦♥❣ ➤ã ●ä✐ > 0✱ ①Ðt ❜➭✐ t♦➳♥ ♣❤ô✿ (B(z0 ) ✭✷✳✶✹✮ + α0 z0 ) − ϕ (z0 ), z }, ∞ i=1 γi Ai ✳ B= z1 ✸✻ ∈ C ✱ α0 > ✈➭ ❧➭ ♥❣❤✐Ư♠ ❝đ❛ ❜➭✐ t♦➳♥ ✭✷✳✶✹✮✳ ❚❤❛② z0 ✱ α0 ✈➭ ❜ë✐ z1 ✱ α1 ✈➭ ➤Ĩ t×♠ z2 ✳ ❚✐Õ♣ tơ❝ q✉➳ tr×♥❤ ➤ã t❛ ❝ã t❤✉❐t t♦➳♥ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ s❛✉✿ • ❚❤✉❐t t♦➳♥ ■■■ (i) ❚➵✐ ❜➢í❝ k = 0✱ ❜➽t ➤➬✉ ✈í✐ z0 ✱ (ii) ❚➵✐ ❜➢í❝ k = n✱ ❜✐Õt zn ✱ ❚×♠ z∈C z∈C B= ●ä✐ zn+1 ✈➭ ✈➭ α0 ❀ αn ✱ ❣✐➯✐ ❜➭✐ t♦➳♥ ♣❤ô s❛✉✿ s❛♦ ❝❤♦✿ min(ϕ(z) + ë ➤➞②✱ n n (B(zn ) + αn zn ) − ϕ (zn ), z ), ✭✷✳✶✺✮ ∞ i=1 γi Ai ✳ ❧➭ ♥❣❤✐Ư♠ ❝đ❛ ❜➭✐ t♦➳♥ (iii) ❉õ♥❣✱ ♥Õ✉ zn+1 − zn ✭✷✳✶✺✮✳ ♥❤á ❤➡♥ ♠ét s❛✐ sè ❝❤♦ tr➢í❝✳ ◆❣➢ỵ❝ ❧➵✐✱ t❤❛② n ←− n + ✈➭ trë ✈Ị ❜➢í❝ (ii)✳ ❙❛✉ ➤➞② ❧➭ ❦Õt q✉➯ ❝❤♦ sù tå♥ t➵✐ ♥❣❤✐Ư♠ ❝đ❛ ❜➭✐ t♦➳♥ ✭✷✳✶✺✮ ✈➭ tÝ♥❤ ❤é✐ tơ tí✐ ♥❣❤✐Ư♠ ➜Þ♥❤ ❧Ý ✷✳✷ u∗ ❝ñ❛ ❜➭✐ t♦➳♥ ✭✷✳✹✮✳ ✭❳❡♠ ❬✻❪✮ ❈❤♦ ❧å✐ ó rỗ ủ t từ C H H ❧➭ ♠ét ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt ✈➭ s❛♦ ❝❤♦ ∞ i=1 F ix(Ti ) F= t❤➢ê♥❣ ✈➭ ❦❤➯ ✈✐ ●➞t❡❛✉① tr➟♥ ✭✷✳✻✮ ✈➭ = ∅✳ ●✐➯ sö r➺♥❣ {γi }∞ i=1 ❧➭ ♠ét ϕ : H −→ R H ✱ ✈í✐ ➤➵♦ ❤➭♠ ϕ ✈➭ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③✳ ❑❤✐ ➤ã✱ ✈í✐ ỗ zn+1 ột t H ọ {Ti }∞ i=1 ❧➭ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ①➵ λi ✲❣✐➯ ❝♦ ❞➲② sè t❤ù❝ t❤á❛ ♠➲♥ ➤✐Ò✉ ❦✐Ö♥ ♥❣❤✐Ö♠ C ❧➭ ♠ét ❤➭♠ ❧å✐ ❝❤Ý♥❤ ❧➭ ♠ét ❤➭♠ ➤➡♥ ➤✐Ö✉ ♠➵♥❤ n ≥ 0✱ ❜➭✐ t♦➳♥ ✭✷✳✶✺✮ ❝ã ❞✉② ♥❤✃t ♠ét ❍➡♥ ♥÷❛✱ ♥Õ✉ ❝➳❝ ❞➲② sè { n }n≥0 ✈➭ {αn }n≥0 t❤á❛ ♠➲♥ ➤✐Ò✉ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✼ Ψ✮ t❤× ❦✐Ö♥ ✭ lim zn = u∗ ∈ F n→∞ ❈❤ø♥❣ ♠✐♥❤✳ ❇➭✐ t♦➳♥ ✭✷✳✶✺✮ t➢➡♥❣ ➤➢➡♥❣ ✈í✐ ❜➭✐ t♦➳♥ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ s❛✉✿ ❚×♠ zn+1 ∈ C ϕ (zn+1 ) + s❛♦ ❝❤♦✿ n (B(zn ) ❚❤❡♦ ❣✐➯ t❤✐Õt ϕ + αn zn ) − ϕ (zn ), v − zn+1 ≥ ∀ v ∈ C ✭✷✳✶✻✮ ❧➭ ❤➭♠ ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ✈➭ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③✱ ♥➟♥ ❜➭✐ t♦➳♥ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ✭✷✳✶✻✮ ❝ã ♠ét ♥❣❤✐Ư♠ ❞✉② ♥❤✃t zn+1 ✳ ❙ư ❞ơ♥❣ ❜✃t ➤➻♥❣ t❤ø❝ t❛♠ ❣✐➳❝ t❛ ❝ã✿ zn+1 − u∗ ≤ zn+1 − uαn + uαn − u∗ , ë ➤➞②✱ uαn ❧➭ ♥❣❤✐Ư♠ ❝đ❛ ❜➭✐ t♦➳♥ ✭✷✳✺✮✱ ✈í✐ ❉♦ ➤ã✱ ➤Ĩ ❝❤ø♥❣ ♠✐♥❤ α = αn limn→∞ zn+1 = u∗ ✈➭ αn → ❦❤✐ n → ∞✳ t❛ ❝➬♥ ❝❤ø♥❣ ♠✐♥❤ ✭✷✳✶✼✮ lim zn+1 − uαn = n→∞ ▼✉è♥ ✈❐② t❛ ①Ðt ♠ét ❤➭♠ s❛✉✿ Φ(u, z) = ϕ(u) − ϕ(z) − ϕ (z), u − z , ë ➤➞②✱ u ✈➭ z t➢➡♥❣ ø♥❣ ♥❤➢ ❧➭ ❚❤❡♦ ❣✐➯ t❤✐Õt✱ ✈× ϕ uαn ✈➭ zn ✳ ❧➭ ❤➭♠ ➤➡♥ ➤✐Ư✉ ♠➵♥❤✱ ♥➟♥ ✈í✐ ♠ä✐ ϕ(u) − ϕ(z) ≥ ϕ (z), u − z + tr♦♥❣ ➤ã✱ ❱➭ ϕ m ❧➭ ❤➺♥❣ sè ➤➡♥ ➤✐Ư✉ ♠➵♥❤ ❝đ❛ ϕ m u−z tr➟♥ ❧➭ ❤➭♠ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③✱ ♥➟♥ ✈í✐ ♠ä✐ t❛ ❝ã✿ ✭✷✳✶✽✮ C✳ u✱ v ∈ C ϕ(u) − ϕ(z) ≤ ϕ (z), u − z + u✱ v ∈ C t❛ ❝ã✿ M u−z 2 ✭✷✳✶✾✮ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com tr♦♥❣ ➤ã✱ M ✸✽ ❧➭ ❤➺♥❣ sè ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③ ❝đ❛ ϕ tr➟♥ C✳ ❚õ ✭✷✳✶✽✮ ✈➭ ✭✷✳✶✾✮ s✉② r❛✿ m u−z 2 ≤ Φ(u, z) ≤ M u−z 2 ➜➷t n = zn − uαn−1 ❙❛✉ ➤➞② t❛ sÏ ❝❤ø♥❣ ♠✐♥❤ r➺♥❣ ❞➲② { ∞ n }n=0 ❜Þ ❝❤➷♥✳ ❚❤❐t ✈❐②✱ t❛ ❝ã ➤➳♥❤ ❣✐➳ s❛✉ Φ(uαn−1 , zn )−Φ(uαn , zn+1 ) ={ϕ(uαn−1 ) − ϕ(zn ) − ϕ (zn ), uαn−1 − zn } − {ϕ(uαn ) − ϕ(zn+1 ) − ϕ (zn+1 ), uαn − zn+1 } =ϕ(uαn−1 ) − ϕ(uαn ) + ϕ (zn+1 ), uαn − zn+1 + ϕ(zn+1 ) − ϕ(zn ) − ϕ (zn ), uαn−1 − zn =ϕ(uαn−1 ) − ϕ(uαn ) + ϕ (zn+1 ), uαn − zn+1 + ϕ(zn+1 ) − ϕ(zn ) − ϕ (zn ), zn+1 − zn − ϕ (zn ), uαn−1 − zn+1 ={ϕ(zn+1 ) − ϕ(zn ) − ϕ (zn ), zn+1 − zn } + {ϕ(uαn−1 ) − ϕ(uαn ) − ϕ (uαn−1 ), uαn−1 − uαn } + ϕ (uαn−1 ), uαn−1 − uαn + ϕ (zn+1 ), uαn − zn+1 − ϕ (zn ), uαn−1 − uαn − ϕ (zn ), uαn − zn+1 ≥ M m zn+1 − zn − uαn−1 − uαn 2 + ϕ (uαn−1 ) − ϕ (zn ), uαn−1 − uαn ✭✷✳✷✵✮ + ϕ (zn+1 ) − ϕ (zn ), uαn − zn+1 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚õ ✭✷✳✺✮ t❤❛② v ❜ë✐ zn+1 ✈➭ t❤❛② ✸✾ α ❜ë✐ αn t❛ ➤➢ỵ❝✿ B(uαn ) + αn uαn , zn+1 − uαn ≥ ❚õ ✭✷✳✶✻✮ t❤❛② v ❜ë✐ ϕ (zn+1 ) + uαn ✭✷✳✷✶✮ t❛ ➤➢ỵ❝✿ n (B(zn ) + αn zn ) − ϕ (zn ), uαn − zn+1 ≥ ✭✷✳✷✷✮ ❚õ ❝➳❝ ❜✃t ➤➻♥❣ t❤ø❝ ✭✷✳✷✶✮ ✈➭ ✭✷✳✷✷✮ s✉② r❛✿ ϕ (zn+1 ) − ϕ (zn ), uαn − zn+1 ≥ n − ▲➵✐ ✈× B(uαn ) + αn uαn , uαn − zn+1 n B(zn ) + αn zn , uαn − zn+1 B ❧➭ ➳♥❤ ①➵ ❧✐➟♥ tơ❝ ▲✐♣s❝❤✐t③ ✈í✐ ❤➺♥❣ sè γ ✱ ♥➟♥ ✈í✐ ♠ä✐ x1 ✱ x2 ∈ C t❛ ❝ã✿ (B(x1 ) + αn x1 ) − (B(x2 ) + αn x2 ) = (B(x1 ) − B(x2 )) + αn (x1 − x2 ) ≤ γ x1 − x2 + αn x1 − x2 ≤ (γ + α0 ) x1 − x2 = L x1 − x2 , ✈í✐ L = γ + α0 ✳ ❚õ ➤ã s✉② r❛ Φ(uαn−1 , zn ) − Φ(uαn , zn+1 ) ≥ E1 + E2 + E3 + E4 , ✭✷✳✷✸✮ tr♦♥❣ ➤ã (B(zn ) + αn zn ) − (B(uαn ) + αn uαn ), zn+1 − zn m zn − zn+1 + = n (B(zn ) + αn zn ) − (B(uαn−1 ) + αn uαn−1 ), zn+1 − zn E1 = n + n (B(uαn−1 ) + αn uαn−1 ) − (B(uαn ) + αn uαn ), zn+1 − zn LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com + m zn − zn+1 ✹✵ 2 m L m 2 zn − zn+1 − n zn − uαn−1 − zn − zn+1 ≥ m 2 L m uαn − uαn−1 − zn − zn+1 − n m 2 L L 2 ≥ n zn − uαn−1 − uαn − uαn−1 ; m m E2 = n (B(zn ) + αn zn ) − (B(uαn ) + αn uαn ), zn − uαn−1 = n (B(zn ) + αn zn ) − (B(uαn−1 ) + αn uαn−1 ), zn − uαn−1 + n (B(uαn−1 ) + αn uαn−1 ) − (B(uαn ) + αn uαn ), zn − uαn−1 ≥r n αn zn − uαn−1 ✈í✐ 2 − nL M zn − uαn−1 − M uαn − uαn−1 ; < r ≤ 1❀ (B(zn ) + αn zn ) − (B(uαn ) + αn uαn ), uαn−1 − uαn M uαn − uαn−1 − = n (B(zn ) + αn zn ) − (B(uαn−1 ) + αn uαn−1 ), uαn−1 − uαn E3 = n + − n (B(uαn−1 ) + αn uαn−1 ) − (B(uαn ) + αn uαn ), uαn−1 − uαn M uαn − uαn−1 2 3M ≥r n αn uαn − uαn−1 − uαn − uαn−1 E4 = ϕ (uαn−1 ) − ϕ (zn ), uαn − uαn−1 ≥ − M uαn−1 − zn L2 2n − zn − uαn−1 M ; uαn − uαn−1 ≥ − c n αn uαn−1 − zn ✈í✐ 2 M uαn − uαn−1 − 4c n αn ; θ = r − c > 0✳ ❚❤❛② E1 ✱ E2 ✱ E3 ✈➭ E4 ✈➭♦ ✭✷✳✷✸✮ t❛ ➤➢ỵ❝✿ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✶ Φ(uαn−1 , zn )−Φ(uαn , zn+1 ) ≥θ n αn uαn−1 − zn (M + 2m) L mM − n uαn−1 − zn (M m + L2 ) uαn − uαn−1 + r n αn uαn − uαn−1 m (M + 2m) 2 2 L n uαn−1 − zn ≥θ n αn uαn−1 − zn − mM (M m + L2 )2 uαn − uαn−1 · − 4rm2 n αn − ❚õ ➤ã s✉② r❛ Φ(uαn , zn+1 ) ≤Φ(uαn−1 , zn ) + [θ n αn uαn−1 − zn + C1 2n + C2 uαn − uαn−1 n αn (M m + L2 )2 ✳ 4rm2 ❚õ ❜✃t ➤➻♥❣ t❤ø❝ tr➟♥✱ ❝❤♦ n ❝❤➵② tõ n = tí✐ n = N ✱ ❧✃② tæ♥❣ N tr♦♥❣ ➤ã C1 = (M + 2m)L2 mM uαn−1 − zn 2 ✈➭ ]; C2 = ❜✃t ➤➻♥❣ t❤ø❝ ➤ã✱ rå✐ ❦Õt ❤ỵ♣ ✈í✐ ✭✷✳✷✵✮ t❛ t❤✉ ➤➢ỵ❝✿ m ( ) 2 n+1 M ≤( ) + C1 ❱❐② s✉② r❛ ❞➲② ➤✐Ị✉ ❦✐Ư♥ ✭Ψ✮✱ { ∞ + [−θ n αn n ✭✷✳✷✹✮ n=1 n αn − αn+1 2 ) · u∗ +C ( n αn ∞ n=1 θ n αn ∞ n }n=1 ❜Þ ❝❤➷♥ ✈➭ ∞ n=1 n αn 2 n ( n αn )−1 ] < ∞✳ ▼➷t ❦❤➳❝✱ t❤❡♦ = ∞ ♥➟♥ tõ ➤➳♥❤ ❣✐➳ tr➟♥ s✉② r❛ lim n→∞ n = 0, ❤❛② lim zn+1 − uαn = n→∞ ❚õ ➤ã s✉② r❛ lim zn+1 − u∗ = n→∞ ➜Þ♥❤ ❧ý ➤➢ỵ❝ ❝❤ø♥❣ ♠✐♥❤✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✷ ❱Ý ❞ô ✷✳✶ ▲✃② < k1 < ✈➭ k2 > s❛♦ ❝❤♦ k1 + k2 < 1✳ ❉➲② {εn } ✈➭ {αn } ợ ị s n = (1 + n)k1 ; αn = (1 + n)−k2 , ❑❤✐ ➤ã ❞➲② {εn } ✈➭ {αn } t❤á❛ ♠➲♥ ➤✐Ị✉ ❦✐Ư♥ s❛✉✿ ➜✐Ị✉ ❦✐Ư♥ Ψ (i) < n (ii) (iii) ≤ 1❀ < αn+1 ≤ αn ≤ 1❀ αn → ❦❤✐ n → ∞❀ ∞ n=0 n αn = ∞❀ ∞ n=0 n < ∞❀ ∞ (αn − αn+1 ) < ∞✳ n=0 αn3 n LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✸ ❑Õt ❧✉❐♥ ▲✉❐♥ trì ữ ề s ã rì ❜➭② ❧➵✐ ♠ét sè ❦✐Õ♥ t❤ø❝ ❝➡ ❜➯♥ ❝ñ❛ ❣✐➯✐ tÝ❝❤ ❤➭♠❀ ❑❤➳✐ ♥✐Ư♠ ✈Ị ❜➭✐ t♦➳♥ t×♠ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ✈➭ sù tå♥ t➵✐ ➤✐Ó♠ ❜✃t ➤é♥❣ tr♦♥❣ ❦❤➠♥❣ ❣✐❛♥ ♠➟tr✐❝❀ ❑❤➳✐ ♥✐Ư♠ ✈Ị ❜➭✐ t♦➳♥ ❝❤Ø♥❤✱ ❜➭✐ t♦➳♥ ➤➷t ❦❤➠♥❣ ❝❤Ø♥❤ ✈➭ ♠ét sè ♣❤➢➡♥❣ ♣❤➳♣ ❤✐Ö✉ ❝❤Ø♥❤✳ • ❚r×♥❤ ❜➭② ❦❤➳✐ ♥✐Ư♠ ✈Ị ❜➭✐ t♦➳♥ ❜✃t ➤➻♥❣ t❤ø❝ ❜✐Õ♥ ♣❤➞♥ ❝ỉ ➤✐Ĩ♥ ✈➭ t❤✉❐t t♦➳♥ ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ t×♠ ♥❣❤✐Ư♠ ❝❤♦ ❜➭✐ t♦➳♥ t tứ ế ổ ể ã rì ♣❤➢➡♥❣ ♣❤➳♣ ❤✐Ư✉ ❝❤Ø♥❤ ➤Ĩ ①➳❝ ➤Þ♥❤ ➤✐Ĩ♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ❣✐➯ ❝♦ t tr rt ã rì tt t ♥❣✉②➟♥ ❧ý ❜➭✐ t♦➳♥ ♣❤ơ ❤✐Ư✉ ❝❤Ø♥❤ ➤Ĩ ①➳❝ ➤Þ♥❤ ➤✐Ó♠ ❜✃t ➤é♥❣ ❝❤✉♥❣ ❝❤♦ ♠ét ❤ä ✈➠ ❤➵♥ ❝➳❝ ➳♥❤ ❣✐➯ ❝♦ ❝❤➷t tr♦♥❣ ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt✳ ❉♦ ✈✃♥ ➤Ị ➤➢ỵ❝ ➤Ị ❝❐♣ tr♦♥❣ ❧✉❐♥ ✈➝♥ ❧➭ t➢➡♥❣ ➤è✐ ♣❤ø❝ t➵♣✱ ❤➡♥ ♥÷❛ ❞♦ t❤ê✐ ❣✐❛♥ ✈➭ ❦❤➯ ♥➝♥❣ ❝đ❛ ❜➯♥ t❤➞♥ ❝ß♥ ❤➵♥ ❝❤Õ ♥➟♥ ♠➷❝ ❞ï ➤➲ ó ề ố ỗ ự s ❧✉❐♥ ✈➝♥ ❦❤➠♥❣ tr➳♥❤ ❦❤á✐ ♥❤÷♥❣ t❤✐Õ✉ sãt✳ ❚➳❝ ❣✐➯ rt ợ ữ ý ế ó ó qí ❜➳✉ ❝đ❛ t❤➬② ❝➠ ❣✐➳♦ ✈➭ ♥❤÷♥❣ ♥❣➢ê✐ q✉❛♥ t➞♠ ➤Ĩ ➤Ị t➭✐ ❤♦➭♥ t❤✐Ư♥ ❤➡♥✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✹ ❚➭✐ ❧✐Ö✉ t❤❛♠ ❦❤➯♦ ❚➭✐ ❧✐Ư✉ t✐Õ♥❣ ❱✐Ưt ❬✶❪ P❤➵♠ ❑ú ❆♥❤✱ ◆❣✉②Ơ♥ ❇➢ê♥❣ ✭✷✵✵✺✮✱ ❇➭✐ t♦➳♥ ➤➷t ❦❤➠♥❣ ❝❤Ø♥❤ ✱ ◆❤➭ ①✉✃t ❜➯♥ ➜➵✐ ọ ố ộ ỗ ❈➳❝ ➤Þ♥❤ ❧Ý ➤✐Ĩ♠ ❜✃t ➤é♥❣ ✱ ◆❤➭ ①✉✃t ❜➯♥ ➜➵✐ ❤ä❝ ❙➢ ♣❤➵♠✳ ❚➭✐ ❧✐Ö✉ t✐Õ♥❣ ❆♥❤ ❬✸❪ ❨❛✳■✳ ❆❧❜❡r✱ ■✳P✳ ❘②❛③❛♥ts❡✈❛ ✭✷✵✵✻✮✱ ◆♦♥❧✐♥❡❛r ✐❧❧✲♣♦s❡❞ ♣r♦❜❧❡♠s ♦❢ ✱ ❙♣r✐♥❣❡r ❱❡r❧❛❣❡✳ ♠♦♥♦t♦♥❡ t②♣❡s ❬✹❪ ❆✳❏✳ ❇❛❛s❛♥s✉r❡♥✱ ❆✳❆✳ ❑❤❛♥ ✭✷✵✵✵✮✱ ✧❘❡❣✉❧❛r✐③❛t✐♦♥ ❛✉①✐❧✐❛r② ♣r♦❜❧❡♠ ♣r✐♥❝✐♣❧❡ ❢♦r ✈❛r✐❛t✐♦♥❛❧ ✐♥❡q✉❛❧✐t✐❡s✧✱ ❛♣♣❧✐❝❛t✐♦♥s ❈♦♠♣✉t❡rs ❛♥❞ ▼❛t❤❡♠❛t✐❝s ✇✐t❤ ✱ ✹✵✱ ♣♣✳ ✾✾✺ ✲ ✶✵✵✷✳ ❬✺❪ ❋✳❊✳ ❇r♦✇❞❡r✱ ❲✳❱✳ P❡tr②s❤②♥ ✭✶✾✻✼✮✱ ✧❈♦♥str✉❝t✐♦♥ ♦❢ ❢✐①❡❞ ♣♦✐♥ts ♦❢ ♥♦♥❧✐♥❡❛r ♠❛♣♣✐♥❣s ✐♥ ❍✐❧❜❡rt s♣❛❝❡s✧✱ ❏✳ ▼❛t❤✳ ❆♥❛❧✳ ❆♣♣❧✳ ✱ ✷✵✱ ♣♣✳ ✶✾✼ ✲ ✷✷✽✳ ❬✻❪ ◆❣✳ ❇✉♦♥❣✱ ▲✳❚✳ ❉✉♦♥❣ ✭✷✵✵✾✮✱ ✧❘❡❣✉❧❛r✐③❛t✐♦♥ ❆✉①✐❧✐❛r② Pr♦❜❧❡♠ ❆❧❣♦✲ r✐t❤♠ ❢♦r ❈♦♠♠♦♥ ❢✐①❡❞ ♣♦✐♥ts ♦❢ ❛ ❝♦✉♥t❛❜❧② ✐♥❢✐♥✐t❡ ❢❛♠✐❧② ♦❢ ♥♦♥✲s❡❧❢ str✐❝t❧② ♣s❡✉❞♦❝♦♥tr❛❝t✐✈❡ ♠❛♣♣✐♥❣s✧✱ ✱ ✸✱ ◆♦✳ ■♥t✳ ❏♦✉r♥❛❧ ♦❢ ▼❛t❤✳ ❆♥❛✳ ✶✶✱ ✺✸✺ ✲ ✺✹✼✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✺ ❬✼❪ ●✳ ❈♦❤❡♥ ✭✶✾✽✵✮✱ ✧❆✉①✐❧✐❛r② ♣r♦❜❧❡♠ ♣r✐♥❝✐♣❧❡ ❛♥❞ ❞❡❝♦♠♣♦s✐t✐♦♥ ♦❢ ♦♣✲ t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s✧✱ ✱ ✸✷✱ ♣♣✳ ✷✼✼ ✲ ✸✵✺✳ ❏✳ ❖♣t✐♠✳ ❚❤❡♦r② ❛♥❞ ❆♣♣❧ ❬✽❪ ●✳ ❈♦❤❡♥ ✭✶✾✽✽✮✱ ✧❆✉①✐❧✐❛r② ♣r♦❜❧❡♠ ♣r✐♥❝✐♣❧❡ ❡①t❡♥❞❡❞ t♦ ✈❛r✐❛t✐♦♥❛❧ ✐♥❡q✉❛❧✐t✐❡s✧✱ ✱ ✺✾✱ ♣♣✳ ✸✵✺ ✲ ✸✷✺ ✳ ❏✳ ❖♣t✐♠✳ ❚❤❡♦r② ❛♥❞ ❆♣♣❧ ❬✾❪ P✳▲✳ ❈♦♠❜❡tt❡s✱ ❙✳❆✳ ❍✐rst♦❛❣❛ ✭✷✵✵✺✮✱ ✧❊q✉✐❧✐❜r✐✉♠ ♣r♦❣r❛♠♠✐♥❣ ✐♥ ❍✐❧❜❡rt s♣❛❝❡s✧✱ ✱ ✻ ✭✶✮✱ ♣♣✳ ❏♦✉r♥❛❧ ♦❢ ◆♦♥❧✐♥❡❛r ❛♥❞ ❈♦♥✈❡① ❆♥❛❧②s✐s ✶✶✼ ✲ ✶✸✻✳ ❬✶✵❪ ❍✳❲✳ ❊♥❣❧✱ ▼✳ ❍❛♥❦❡ ❛♥❞ ❆✳ ◆❡✉❜❛✉❡r ✭✶✾✾✻✮✱ Pr♦❜❧❡♠s ❘❡❣✉❧❛r✐③❛t✐♦♥ ♦❢ ■♥✈❡rs❡ ✱ ❑❧✉✇❡r ❉♦r❞r❡❝❤t✳ ❬✶✶❪ ◆✳❊✳ ❋❛r♦✉q ✭✷✵✶✶✮✱ ✧Ps❡❞♦♠♦♥♦t♦♥❡ ✈❛r✐❛t✐♦♥❛❧ ✐♥❡q✉❛❧✐t✐❡s✿ ❈♦♥✈❡r✲ ❣❡♥❝❡ ♦❢ t❤❡ ❛✉①✐❧✐❛r② ♣r♦❜❧❡♠ ♠❡t❤♦❞✧✱ ✶✶✶✱ ❏✳ ❖♣t✐♠✳ ❚❤❡♦r② ❛♥❞ ❆♣♣❧✳ ✱ ♣♣✳ ✸✵✺ ✲ ✸✷✻✳ ❬✶✷❪ ❉✳ ❑✐♥❞❡r❧❡❤r❡r✱ ●✳ ❙t❛♠♣❛❝❝❤✐❛ ✭✶✾✽✵✮✱ ■♥❡q✉❛❧✐t✐❡s ❛♥❞ ❚❤❡✐r ❆♣♣❧✐❝❛t✐♦♥s ❆♥ ✐♥tr♦❞✉❝t✐♦♥ t♦ ❱❛r✐❛t✐♦♥❛❧ ✱ ❆❝❛❞❡♠✐❝ Pr❡ss✳ ❬✶✸❪ ●✳ ▼❛str♦❡♥✐ ✭✷✵✵✵✮✱ ✧❖♥ ❛✉①✐❧✐❛r② ♣r✐♥❝✐♣❧❡ ❢♦r ❡q✉✐❧✐❜r✐✉♠ ♣r♦❜❧❡♠s✧✱ ❚❡❝❤♥✐❝❛❧ ❘❡♣♦rt ♦❢ t❤❡ ❞❡♣❛rt♠❡♥t ♦❢ ♠❛t❤❡♠❛t✐❝s ♦❢ P✐s❛ ❯♥✐✈❡rs✐t②✱ ✱ ✸✱ ♣♣✳ ✶✷✹✹ ✲ ✶✷✺✽ ✳ ■t❛❧② ❬✶✹❪ ▼✳❖✳ ❖s✐❧✐❦❡✱ ❆✳ ❯❞♦♠❡♥❡ ✭✷✵✵✶✮✱ ✧❉❡♠✐❝❧♦s❡❞♥❡ss ♣r✐♥❝✐♣❧❡ ❛♥❞ ❝♦♥✲ ✈❡r❣❡♥❝❡ t❤❡♦r❡♠s ❢♦r str✐❝t❧② ♣s❡✉❞♦❝♦♥tr❛❝t✐✈❡ ♠❛♣♣✐♥❣s✧✱ ❏✳ ▼❛t❤✳ ✱ ✷✺✻✱ ♣♣✳ ✹✸✶ ✲ ✹✹✺✳ ❆♥❛❧✳ ❆♣♣❧✳ ❬✶✺❪ ❯✳ ❚❛✉t❡♥❤❛❤♥ ✭✷✵✵✹✮✱ ✧▲❛✈r❡♥t✐✈❡ r❡❣✉❧❛r✐③❛t✐♦♥ ♦❢ ♥♦♥❧✐♥❡❛r ✐❧❧✲♣♦s❡❞ ♣r♦❜❧❡♠✧✱ ❱✐❡t♥❛♠ ❏♦✉r♥❛❧ ♦❢ ▼❛t❤❡♠❛t✐❝s ✱ ✸✷✱ ♣♣✳ ✷✾ ✲ ✹✶✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ...ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC SƯ PHẠM ĐÀM THỊ HỒNG NGUN LÝ BÀI TỐN PHỤ HIỆU CHỈNH TÌM ĐIỂM BẤT ĐỘNG CHUNG CHO MỘT HỌ VÔ HẠN ÁNH XẠ GIẢ CO CHẶT Chun ngành: TỐN GIẢI TÍCH Mã số: 60.46.01.02 LUẬN... TÍCH Mã số: 60.46.01.02 LUẬN VĂN THẠC SĨ TOÁN HỌC Người hướng dẫn khoa học: TS LÂM THÙY DƯƠNG THÁI NGUYÊN - 2016 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✶ ▼ô❝ ❧ô❝ ▲ê✐ ❝❛♠ ➤♦❛♥... ❚❤Þ ❍å♥❣ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✐✐ ▼ô❝ ❧ô❝ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✈ ▼ét sè ❦ý ❤✐Ö✉ ✈➭ ✈✐Õt t➽t H ❦❤➠♥❣ ❣✐❛♥ ❍✐❧❜❡rt t❤ù❝ E