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Code 

 y[1] = 1;
 y[2] = 2;
 y[3] = 3;
 Min[y[1], y[2], y[3]]

Outputs "1", but desired result is y[1]

How to do that? Many thanks for help.

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You can get the value(s) i for which y[i] is minimal :

 y[1] = 10;
 y[2] = 20;
 y[3] = 30;
 MinimalBy[Range[3],y]

{1}

But as soon as you wrap the result 1 in y[...], y[1] will be evaluated to 10, accordingly to the princips of Mathematica.

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  • $\begingroup$ HoldForm[y[n]] /. n -> First@MinimalBy[Range[3], y] gives y[1] $\endgroup$ – bbgodfrey Jul 29 '17 at 3:01
  • $\begingroup$ @bbgodfrey Your answer help me a lot. Many thanks. $\endgroup$ – Robin_Lyn Jul 29 '17 at 3:20
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For the exact example given you could perhaps utilize the DownValues list:

MinimalBy[DownValues[y], Last][[1, 1]]

HoldPattern[y[1]]
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