Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Các định lý điểm cố định ngẫu nhiên dựa trên các đặc điểm của topologie yếu và ứng dụng vào các phương trình tích phân ngẫu nhiên với sự thiếu vắng tính chặt chẽ
Tóm tắt
Chúng tôi trình bày một số định lý điểm cố định ngẫu nhiên cho các toán tử ngẫu nhiên với miền xác định có tính chất xác định hoặc ngẫu nhiên. Các giả thuyết chính của kết quả của chúng tôi được hình thành dưới dạng topologie yếu và định nghĩa theo định đề về thang đo sự không chặt chẽ yếu. Các kết quả này mở rộng theo một cách rộng rãi một số kết quả mới và cổ điển trong tài liệu. Như một ứng dụng, chúng tôi thảo luận về khả năng giải của phương trình tích phân Hammerstein ngẫu nhiên với sự thiếu vắng tính chặt chẽ.
Từ khóa
#định lý điểm cố định ngẫu nhiên #toán tử ngẫu nhiên #topologie yếu #phương trình tích phân Hammerstein #tính chặt chẽTài liệu tham khảo
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