设f(x)定义在(a,b)上.当x1,x2∈(a,b),P1,p2∈[0,1]且P1+P2=1时,f(P1x1+P2x2)≤P1f(x1)+p2f(x2),试证:当x1,x2,…
设f(x)定义在(a,b)上.当x1,x2∈(a,b),P1,p2∈[0,1]且P1+P2=1时,f(P1x1+P2x2)≤P1f(x1)+p2f(x2),试证:当x1,x2,…,xn∈(a,b),P1,p2,…,pn,∈[0,1],且.P1+p2+…+pn=1时,f(p1x1+P2x2+…+pnxn)≤P1f(x1)+p2f(x2)+…+Pnf(xn)