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A new approach to Ky Fan type inequalities | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 28 بهمن 1404 اصل مقاله (345.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2026.40161.5606 | ||
| نویسنده | ||
| Jamal Rooin* | ||
| Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran | ||
| تاریخ دریافت: 03 دی 1404، تاریخ پذیرش: 24 دی 1404 | ||
| چکیده | ||
| In this article, using a discrete method, we get some new interesting recursive identities concerning arithmetic, geometric, and harmonic means of positive numbers, from which, the most important Ky Fan-type inequalities are handled by induction at once. | ||
| کلیدواژهها | ||
| AGM inequality؛ Ky Fan’s inequality؛ Mean value theorem | ||
| مراجع | ||
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[1] H. Alzer, Ungleichungen für geometrische und arithmetische Mittelwerte, Proc. Kon. Nederl. Akad. Wetensch. 91 (1988), 365–374.
[2] H. Alzer, Inequalities for arithmetic, geometric and harmonic means, Bull. London Math. Soc. 22 (1990), 362–366.
[3] H. Alzer, The inequality of Ky Fan and related results, Acta Appl. Math. 38 (1995), 305–354.
[4] E.F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin, 1961.
[5] P.S. Bullen, D.S. Mitrinovi´c, and P.M. Vasi´c, Means and Their Inequalities, Reidel, Dordrecht, 1988.
[6] J. Rooin, On Ky Fan’s inequality and its additive analogues, Math. Inequal. Appl. 6 (2003), no. 4, 595–604.
[7] J. Rooin, Some new proofs for the AGM inequality, Math. Inequal. Appl. 7 (2004), no. 4, 517–521.
[8] J. Rooin, An approach to Ky Fan type inequalities from binomial expansions, Math. Inequal. Appl. 11 (2008), no. 4, 679–688.
[9] J. Rooin, Ky Fan’s inequality via convexity, J. Inequal. Pure Appl. Math. 9 (2008), no. 1, Article 23.
[10] J. Rooin and A. R. Medghalchi, New proofs for Ky Fan’s inequality and two of its variants, Int. J. Appl. Math. 10 (2002), no. 1, 51–57.
[11] W.L. Wang and P.F. Wang, A class of inequalities for the symmetric functions, Acta Math. Sinica 27 (1984), 485–497. [In Chinese] | ||
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