Wu, Shanhe; Debnath, Lokenath Inequalities for differences of power means in two variables. (English) Zbl 1240.26069 Anal. Math. 37, No. 2, 151-159 (2011). Summary: Using classical analytic techniques, a double inequality for differences of power means and geometric means in two variables is generalized and sharpened. A new inequality for differences of power means involving four parameters is established. Cited in 1 ReviewCited in 5 Documents MSC: 26E60 Means 26D20 Other analytical inequalities Keywords:inequalities for differences of means; arithmetic mean; geometric mean; power mean PDFBibTeX XMLCite \textit{S. Wu} and \textit{L. Debnath}, Anal. Math. 37, No. 2, 151--159 (2011; Zbl 1240.26069) Full Text: DOI References: [1] P. S. Bullen, D. S. Mitrinović, and P. M. Vasić, Means and Their Inequalities, Kluwer Academic Publishers (Dordrecht, 1988). · Zbl 0687.26005 [2] P. S. Bullen, Handbook of Means and their Inequalities, Kluwer Academic Publishers (Dordrecht, 2003). · Zbl 1035.26024 [3] J. Sándor, A note on some inequalities for means, Arch. Math. (Basel), 56(1991), 471–473. · Zbl 0693.26005 · doi:10.1007/BF01200091 [4] W. Janous, A note on generalized Heronian means, Math. Inequal. Appl., 4(3)(2001), 369–375. · Zbl 1128.26302 [5] B. C. Carlson, The logarithmic mean, Amer. Math. Monthly, 79 (1972), 615–618. · Zbl 0241.33001 · doi:10.2307/2317088 [6] G. Pólya and G. Szego, Isoperimetric inequalities in mathematical physics (Annals of Mathematics Studies, 27), Princeton Univ. Press (1951). · Zbl 0044.38301 [7] S. Wu, Generalization and sharpness of power means inequality and their applications, J. Math. Anal. Appl., 312(2005), 637–652. · Zbl 1083.26018 · doi:10.1016/j.jmaa.2005.03.050 [8] S. Wu, On a weighted and exponential generalization of Rado’s inequality, Taiwan. J. Math., 13(1)(2009), 359–368. · Zbl 1179.26083 [9] S. Wu and L. Debnath, Weighted generalization of Rado’s inequality and Popoviciu’s inequality, Appl. Math. Lett., 21(4)(2008), 313–319. · Zbl 1133.26313 · doi:10.1016/j.aml.2007.03.017 [10] H. Alzer and S.-L. Qiu, Inequalities for means in two variables, Arch. Math. (Basel), 80(2003), 201–215. · Zbl 1020.26011 · doi:10.1007/s00013-003-0456-2 [11] L. Zhu, New inequalities for means in two variables, Math. Inequal. Appl., 11(2)(2008), 229–235. · Zbl 1141.26317 [12] L. Zhu, Some new inequalities for means in two variables, Math. Inequal. Appl., 11(3)(2008), 443–448. · Zbl 1154.26029 [13] A. McD. Mercer, Bounds for A-G, A-H, G-H, and a family of inequalities of Ky Fan’s type, using a general method, J. Math. Anal. Appl., 243(2000), 163–173. · Zbl 0944.26027 · doi:10.1006/jmaa.1999.6688 [14] J. Sándor and T. Trif, Some new inequalities for means of two arguments, Int. J. Math. Math. Sci., 25(2001), 525–532. · Zbl 1002.26018 · doi:10.1155/S0161171201003064 [15] T. Trif, Note on certain inequalities for means in two variables, J. Inequal. Pure Appl. Math., 6(2)(2005), Article 43, 1–5 (electronic). · Zbl 1073.26019 [16] O. Kouba, New bounds for the identric mean of two arguments, J. Inequal. Pure Appl. Math., 9(3)(2008), Article 71, pp.1–6 (electronic). · Zbl 1172.26314 [17] G. D. Anderson, S. L. Qiu, M. K. Vamanamurthy, and M. Vuorinen, Generalized elliptic integrals and modular equations, Pacific J. Math., 192(1)(2000), 1–37. · Zbl 0951.33012 · doi:10.2140/pjm.2000.192.1 [18] G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, Conformal Invariants, Inequalities, and Quasiconformal Maps Canadian Math. Soc., Series of Monographs and Advanced Texts, John Wiley and Sons (New York, 1997). [19] D. S. Mitrinović and P. M. Vasić, Analytic Inequalities, Springer (Berlin-New York-Heidelberg, 1970). · Zbl 0213.22303 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.