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ЖУРНАЛЫ // Алгебра и анализ
Алгебра и анализ, 2023, том 35, выпуск 6, страницы 169–191 (Mi aa1896)
Неравенства между смешанными средними
А. И. Храбров

Список литературы
1. Беккенбах Э., Беллман Р., Неравенства, Мир, М., 1965
2. Богачев В. И., Основы теории меры, т. 1, РХД, Ижевск, 2003
3. Либ Э., Лосс М., Анализ, Науч. кн., Новосибирск, 1998
4. Петров А. Н., “Монотонность усредненных средних степенных”, Зап. науч. семин. ПОМИ, 255, 1998, 140–147  mathnet  zmath
5. Харди Г. П., Литтльвуд Д. Е., Полиа Г., Неравенства, ИЛ, М., 1948
6. de Brujn N. G., “Carleman's inequality for finite series”, Nederl. Akad. Wetensch. Proc. Ser. A 66 Indag. Math., 25 (1963), 505–514  crossref  mathscinet
7. Bullen P. S., Mitrinović D. S., Vasić P. M., Means and their inequalities, Math. Appl. (East Eur. Ser.), 31, D. Reidel Publ. Co., Dordrecht, 1988  mathscinet  zmath
8. Bullen P. S., Handbook of means and their inequalities, Math. Appl., 560, Kluwer Acad. Publ. Group, Dordrecht, 2003  mathscinet  zmath
9. Carleman T., “Sur les fonctions quasi-analytiques”, Conférences faites au cinquième congrès des math. Scandinaves (Juillet, 1922), Librairie Académique, Helsingfors, 1923, 181–196
10. Carleson L., “A proof of an inequality of Carleman”, Proc. Amer. Math. Soc., 5 (1954), 932–933  crossref  mathscinet  zmath
11. Čižmešija A., Pečarić J., “Mixed means and Hardy's inequality”, Math. Ineq. Appl., 1:4 (1998), 491–506  mathscinet
12. Čižmešija A., Pečarić J., “Classical Hardy's and Carleman's inequalities and mixed means”, Math. Appl., 517, Kluwer Acad. Publ., 2000, 27–65  mathscinet
13. Čižmešija A., Pečarić J., Persson L.-E., “On strengthened Hardy and Pólya–Knopp's inequalities”, J. Approx. Theory, 125:1 (2003), 74–84  crossref  mathscinet
14. Duncan J., McGregor C. M., “Carleman's inequality”, Amer. Math. Monthly, 110:5 (2003), 424–431  crossref  mathscinet  zmath
15. Hardy G. H., “Remarks on three recent notes in the journal”, J. London Math. Soc., 3:3 (1928), 166–169  crossref  mathscinet
16. Hardy G. H., “Prolegomena to a chapter of inequalities”, J. London Math. Soc., 4:1 (1929), 61–78  crossref  mathscinet
17. Holland F., “On a mixed arithmetic-mean, geometric-mean inequality”, Math. Competit., 5 (1992), 60–64
18. Holland F., “An inequality between compositions of weighted arithmetic and geometric means”, JIPAM. J. Inequal. Pure Appl. Math., 7:5 (2006), 159, 8 pp.  mathscinet  zmath
19. Johansson M., Persson L.-E., Wedestig A., “Carleman's inequality — history, proofs and some new generalizations”, JIPAM. J. Inequal. Pure Appl. Math., 4:3 (2003), 53, 19 pp.  mathscinet  zmath
20. Kaijser S., Persson L.-E., Öberg A., “On Carleman's and Knopp's inequalities”, J. Approx. Theory, 117:1 (2002), 140–151  crossref  mathscinet  zmath
21. Kedlaya K., “Proof of a mixed arithmetic-mean, geometric-mean inequality”, Amer. Math. Monthly, 101:4 (1994), 355–357  mathscinet  zmath
22. Kedlaya K., “A weighted mixed-mean inequality”, Amer. Math. Monthly, 106:4 (1999), 355–358  crossref  mathscinet  zmath
23. Knopp K., “Über reihen mit positivern gliedern”, J. London Math. Soc., 3:3 (1928), 205–211  crossref  mathscinet
24. Kufner A., Persson L.-E., Samko N., Weighted inequalities of Hardy type, Second ed., World Sci. Publ. Co., Hackensack, NJ, 2017  mathscinet  zmath
25. Lai B., Wang R., Liu H., “A note on two weighted discrete Carleman inequalities”, J. Math. Ineqal., 15:4 (2021), 1601–1611  mathscinet  zmath
26. Matsuda T., “An inductive proof of a mixed arithmetic-geometric mean inequality”, Amer. Math. Monthly, 102:7 (1995), 634–637  crossref  mathscinet  zmath
27. Mitrinović D. S., Pečarić J. E., Fink A. M., Inequalities involving functions and their integrals and derivatives, Math. Appl. (East Eur. Ser.), 53, Kluwer Acad. Publ. Group, Dordrecht, 1991  mathscinet  zmath
28. Mond B., Pečarić J. E., “A mixed means inequality”, Austral. Math. Soc. Gaz., 23:2 (1996), 67–70  mathscinet  zmath
29. Pečarić J., Stolarsky K., “Carleman's inequality: history and new generalizations”, Aequationes Math., 61:1-2 (2001), 49–62  crossref  mathscinet
30. Pólya G., “Proof of an inequality”, Proc. London Math. Soc. Ser. 2, 24 (1926), LVII
31. Redheffer R. M., “Recurrent inequalities”, Proc. London Math. Soc. Ser. 3, 17:4 (1967), 683–699  crossref  mathscinet  zmath
32. Sunouchi G., Takagi N., “A generalization of the Carleman's inequality theorem”, Proc. Phys.-Math. Soc. Japan, 16 (1934), 164–166  zmath
33. Tarnavas C., Tarnavas D., “An inequality for mixed power means”, Math. Ineqal. Appl., 2:2 (1999), 175–181  mathscinet  zmath

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