Generalizations of the Jensen-Steffensen and related inequalities

• Autorzy: Milica Bakula , Marko Matić , Josip Pečarić
• Języki publikacji: EN

Abstrakty

EN

We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.

Słowa kluczowe

EN

Convex functions; Jensen-Steffensen inequality; Slater’s inequality

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 787-803

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Milica Bakula

• Faculty of Science, Department of Mathematics, University of Split, Split, Croatia

autor

Marko Matić

• Faculty of Science, Department of Mathematics, University of Split, Split, Croatia

autor

Josip Pečarić

• Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia

Bibliografia

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• [6] Elezović N., Pečarić J., A counterpart to Jensen-Steffensen’s discrete inequality for differentiable convex mappingsand applications in information theory, Rad Hrvat. Akad. Znan. Umjet., 2003, 481(14), 25–28
• [7] Matić M., Pečarić J., Some companion inequalities to Jensen’s inequality, Math. Inequal. Appl., 2000, 3(3), 355–368
• [8] Pečarić J., A companion to Jensen-Steffensen’s inequality, J. Approx. Theory, 1985, 44(3), 289–291 http://dx.doi.org/10.1016/0021-9045(85)90099-1[Crossref]
• [9] Pečarić J., A multidimensional generalization of Slater’s inequality, J. Approx. Theory, 1985, 44(3), 292–294 http://dx.doi.org/10.1016/0021-9045(85)90100-5[Crossref]
• [10] Roberts A.W., Varberg D.E., Convex functions, Academic Press, New York-London, 1973
• [11] Slater M.L., A companion inequality to Jensen’s inequality, J. Aprox. Theory, 1981, 32(2), 160–166 http://dx.doi.org/10.1016/0021-9045(81)90112-X[Crossref]
• [12] Steffensen J.F., On certain inequalities and methods of approximation, J. Inst. Actuaries, 1919, 51, 274–297

Identyfikatory

DOI

10.2478/s11533-009-0052-1