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abx1x2x11x2fx11x2fx11fx2Figure1fisconvexonabiffx11x2fx11fx28x1x22ab2012ConvexFunctionsDe nition1Letfbearealvaluedfunctionde nedonanintervalIa

abx1x2x1+(1)x2f(x1+(1)x2)f(x1)+(1)f(x2)Figure1:fisconvexon[a;b]iff(x1+(1)x2)f(x1)+(1)f(x2)8x1;x22[a;b];2[0;1]:2ConvexFunctionsDe nition1Letfbearealvaluedfunctionde nedonanintervalI=[a

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