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证明施瓦茨(Schwarz)不等式:若f和g在[a,b]上可积,则
证明施瓦茨(Schwarz)不等式:若f和g在[a,b]上可积,则
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证明:若函数f(x,y)在开区域G对变量x连续,对变量y满足利普希茨条件,即有|f(x,y1)-f(x,y2)|≤L|y1-y2|,
其中L是常数,则函数f(x,y)在G连续.
(Jensen不等式)设f(x)为[a,b]上的连续下凸函数,证明对于任意xi∈[a,b]和名γi>0(i=1,2,...,n),,成立