Shapiro proposed an inequality in the 1954 American Mathematical Monthly, which now goes by his name. The inequality is now settled but work on the subject continues. The discussion of the history of this inequality does not always give a clear picture of the chronology and the results. In addition, the work still to be done is not always made clear. Here, we try to separate the various aspects of the problem: give the chronology and priorities; give a hint on the role of computer proofs; give the shortest route to the results; indicate the methods used in the shortest route; conjecture about the continued interest in the problem; and indicate where further work can be done.
Key words and phrasesCyclic inequality History
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