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Is there a comprehensive reference book on inequalities in the spirit of the one written by G.H. Hardy, J.E. Littlewood, and G. Pólya(*), but more up-to-date (i.e., published in more recent years and with both well-established results and novel developments)?

(*) Clarification

The following description is taken from the publisher's website:

"This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians."

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    $\begingroup$ How about "The Cauchy-Schwarz Master Class" by J. Michael Steele, Cambridge University Press 2004? $\endgroup$
    – Stopple
    Commented Mar 10, 2015 at 14:47
  • $\begingroup$ @Stopple, I've heard of it, but I'm not sure that it is at the same level as the book mentioned above. Do you have any information? $\endgroup$
    – user60665
    Commented Mar 10, 2015 at 14:47
  • $\begingroup$ Would anyone explain why this is "primarily opinion based"? I honestly don't get it. $\endgroup$
    – user60665
    Commented Mar 11, 2015 at 17:34
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    $\begingroup$ Another useful reference is Mitrinovic's monograph Analytic inequalities. books.google.com/… $\endgroup$
    – Liviu Nicolaescu
    Commented Mar 11, 2015 at 19:39

2 Answers 2

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I think that the following book is a very nice 'grandson' of the one written by Hardy, Littlewood, and Pólya:

D.J.H. GARLING, Inequalities. A Journey into Linear Analysis, Cambridge University Press, 2007.

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    $\begingroup$ Thanks for the suggestion. Could you add to your answer some information about this book and a brief description? $\endgroup$
    – user60665
    Commented Mar 10, 2015 at 15:59
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    $\begingroup$ The book is by: "D. J. H. Garling" and not Ben Garling. It's a really nice book though. $\endgroup$
    – Suvrit
    Commented Mar 10, 2015 at 18:22
  • $\begingroup$ Dear @Suvrit, could you add some comments on this book? $\endgroup$
    – user60665
    Commented Mar 10, 2015 at 20:45
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    $\begingroup$ @Dal: please have a look at it here: books.google.com/… $\endgroup$
    – Suvrit
    Commented Mar 10, 2015 at 20:52
  • $\begingroup$ @Suvrit He does call himself Ben though, just in case anyone is wondering if it is that same Garling. $\endgroup$
    – Thompson
    Commented Apr 19, 2017 at 15:30
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Albert W. Marshall, Ingram Olkin, Barry C. Arnold: "Inequalities: Theory of Majorization and Its Applications" , second edition, Springer, fits the bill. They explicitely name the Hardy et al book as an ancestor and inspirator.

The book is based on the concept of majorization and some extension of that, which they say, is literally a "theory of inequalities" and functions as an organizing tool.

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