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2009 | 7 | 4 | 787-803
Tytuł artykułu

Generalizations of the Jensen-Steffensen and related inequalities

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
787-803
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
  • Faculty of Science, Department of Mathematics, University of Split, Split, Croatia
autor
  • Faculty of Science, Department of Mathematics, University of Split, Split, Croatia
  • Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
Bibliografia
  • [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]
  • [2] Boas R.P., The Jensen-Steffensen inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., 1970, 302–319, 1–8
  • [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]
  • [4] Dragomir S.S., On a converse of Jensen’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 2001, 12(2), 48–51
  • [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
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0052-1
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