Let $~a\lt b\lt c\lt d$，proof that if $f$ is a convex function both in $[a,c]$ and $[b,d]$, $f$ is convex in $[a,d]$

Asked Jul 23 '19 at 09:24

Active Jul 23 '19 at 09:34

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This is a problem from mathematical analysis.

It is clear that we only need to discuss the the problem when $x_1$, $x_2$ are located in $[a,b]$ and $[c,d]$ respectively.

I have tried mark $x_0$ in $[b,c]$ as I think this may help me use the definition of convex function.

(I am sorry that my English is poor, thank you very much)

edited Jul 23 '19 at 09:34

nmasanta

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asked Jul 23 '19 at 09:24

Z.B. Zuo

490

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Jul 23 '19 at 09:26
Possible duplicate of How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$). – Martin R Jul 23 '19 at 09:40

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