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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0052-1,
author = {Milica Bakula and Marko Mati\'c and Josip Pe\v cari\'c},
title = {Generalizations of the Jensen-Steffensen and related inequalities},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {787-803},
zbl = {1183.26020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0052-1}
}
Milica Bakula; Marko Matić; Josip Pečarić. Generalizations of the Jensen-Steffensen and related inequalities. Open Mathematics, Tome 7 (2009) pp. 787-803. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0052-1/
[1] Abramovich S., Klaričić Bakula M., Matić M., Pečarić J., A variant of Jensen-Steffensen’s inequality and quasi-arithmetic means, 2005, J. Math. Anal. Appl., 307, 370–386 http://dx.doi.org/10.1016/j.jmaa.2004.10.027[Crossref] | Zbl 1066.26012
[2] Boas R.P., The Jensen-Steffensen inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 1970, 302–319, 1–8 | Zbl 0213.34601
[3] Dragomir S.S., Goh C.J., A counterpart of Jensen’s discrete inequality for differentiable convex mappings and applications in information theory, Math. Comput. Modelling, 1996, 24(2), 1–11 http://dx.doi.org/10.1016/0895-7177(96)00085-4[Crossref] | Zbl 0862.94010
[4] Dragomir S.S., On a converse of Jensen’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 2001, 12(2), 48–51 | Zbl 1054.26017
[5] Dragomir S.S., Ionescu N.M., Some converse of Jensen’s inequality and applications, Rev. Anal. Numér. Théor. Approx., 1994, 23(1), 71–78 | Zbl 0836.26009
[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 | Zbl 0968.26015
[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 | Zbl 0271.26009
[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