Accentuate the negative
Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 427-446

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MR Zbl
A survey of mean inequalities with real weights is given.
A survey of mean inequalities with real weights is given.
DOI : 10.21136/MB.2009.140674
Classification : 26D15, 26E60
Keywords: convex functions; Jensen inequality; Jensen-Steffensen inequality; real weights; reverse inequality
Bullen, P. S. Accentuate the negative. Mathematica Bohemica, Tome 134 (2009) no. 4, pp. 427-446. doi: 10.21136/MB.2009.140674
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[1] Abramovich, S., Klaričić Bakula, M., Matić, M., Pečarić, J.: A variant of Jensen-Steffensen's inequality and quasi-arithmetic means. J. Math. Anal. Appl. 307 (2005), 370-386. | DOI | MR | Zbl

[2] Aczél, J.: Some general methods in the theory of functional equations in one variable. New applications of functional equations. Uspehi Mat. Nauk (N.S.) 11 (1956), 3-68. | MR

[3] Alzer, Horst: Inequalities for pseudo arithmetic and geometric means. General Inequalities 6 5-16 (Oberwolfach 1990). | MR | Zbl

[4] Beckenbach, Edwin F., Bellman, Richard: Inequalities. Springer, Berlin (1961). | MR | Zbl

[5] Bullen, P. S.: The Jensen-Steffensen inequality. Math. Ineq. Appl. 1 (1998), 391-401. | MR | Zbl

[6] Bullen, P. S.: Handbook of Means and Their Inequalities. Kluwer Academic Publishers, Dordrecht (2003). | MR | Zbl

[7] Daróczy, Zoltán, Páles, Zsolt: On a class of means of several variables. Math. Ineq. Appl. 4 (2001), 331-334. | MR | Zbl

[8] Hardy, G. H., Littlewood, E. J., Pólya, G.: Inequalities. Cambridge University Press, Cambridge (1934).

[9] Landsberg, P. T., Pečarić, E. J.: Thermodynamics, inequalities and negative heat capacities. Phys. Rev. A35 (1987), 4397-4403. | DOI

[10] Marshall, Albert W., Olkin, Ingram: Inequalities: Theory of Majorization and Its Applications. Academic Press, New York (1979). | MR | Zbl

[11] Matković, Anita, Pečarić, Josip: A variant of Jensen's inequality for convex functions of several variables. J. Math. Ineq. 1 (2007), 45-51. | DOI | MR | Zbl

[12] Mitrinović, D. S., Pečarić, E. J., Fink, M. A.: Classical and New Inequalities in Analysis. Reidel, Dordrecht (1993).

[13] Nanjundiah, T. S.: Sharpening some classical inequalities. Math. Student 20 (1952), 24-25.

[14] Pečari'c, J. E.: Inverse of Jensen-Steffensen inequality. Glasnik Mat. 16 (1981), 229-233. | MR

[15] Pečari'c, Josip E.: A new proof of the Jensen-Steffensen inequality. Mathematica Rév. Anal. Num. Théorie Appr. 23 (1981), 73-77. | MR

[16] Pečari'c, J. E.: Inverse of Jensen-Steffensen inequality. (II), Glasnik Mat. 19 (1984), 235-238. | MR

[17] Pečari'c, Josip E.: A simple proof of the Jensen-Steffensen inequality. Amer. Math. Monthly 91 (1984), 195-196. | DOI | MR

[18] Pečari'c, Josip E.: Notes on Jensen's inequality. General Inequalities 6 (Oberwolfach, 1990) 449-454 Internat. Ser. Numer. Math., 103, Birkhäuser, Basel (1992). | MR

[19] Pečarić, Josip E., Proschan, Frank, Tong, L. Y.: Convex Functions, Partial Orderings and Statistical Applications. Academic Press, New York (1992). | MR

[20] Wayne, Roberts, A., Varberg, Dale E.: Convex Functions. Academic Press, New York (1973). | MR

[21] Steffensen, J. F.: On certain inequalities and methods of approximation. J. Inst. Actuar. 51 (1919), 274-297. | DOI

[22] Vasić, Petar M., Pečarić, Josip E.: On the Jensen inequality. Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 634--No. 677 (1979), 50-54. | MR

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