Cauchy-Schwarz不等式的一个加强

摘要

设f(x),g(x)均在[a,b]上可积,则Cauchy-Schwarz不等式可加强为:[∫baf(x)g(x)dx]2 ≤∫baf2(x)dx∫ba g2(x)dx + 2/b-a∫ba f(x)g(x)dx∫ba f(x)d(x)∫ba g(x)dx - 1/b-a∫ba f2(x)dx ·[∫ba g(x)dx]2-1/b-a∫ba g2(x)dx[∫ba f(x)dx]2.由此推广了文[1]结果