On convexity-like inequalities (II)

Authors

  • Josip Pečarić University of Zagreb, Croatia
  • Sanja Varošanec University of Zagreb, Croatia

DOI:

https://doi.org/10.33993/jnaat321-737

Keywords:

Jensen's inequality, convexity-like inequalities, generalized Steffensen's inequality
Abstract views: 177

Abstract

We improve the classical Jensen inequality for convex functions by extending it to a wider class of functions. We also consider some weaker conditions for the weights occurring in this inequality.

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References

Dragomirescu, M. and Ivan, C., Convexity-like inequalities for averages in a convex set, Aequationes Math., 45, pp. 179-199, 1993, https://doi.org/10.1007/BF01855877. DOI: https://doi.org/10.1007/BF01855877

Mitrinović, D. S., Pečarić, J. and Fink, A. M., Classical and New Inequalities in Analysis, Kluwer Acad. Publ., Dordrecht, 1993. DOI: https://doi.org/10.1007/978-94-017-1043-5

Pearce, C. E. M. and Pečarić, J., On convexity--like inequalites, Rev. Roumaine Math. Pure Appl., 42, nos. 1-2, pp. 133-138, 1997.

Pečarić, J., A simple proof of the Jensen--Steffensen inequality, Amer. Math. Monthly, 91, pp. 195-196, 1984, https://doi.org/10.1080/00029890.1984.11971374. DOI: https://doi.org/10.1080/00029890.1984.11971374

Pečarić, J., On the Jensen--Steffensen inequality, Univ. Beograd, Publ. ETF, 634-677, pp. 101-107, 1979.

Pečarić, J., Proschan, F. and Tong, Y. L., Convex functions, Partial Orderings and Statistical Applications, Academic Press, 1992.

Pečarić, J. and Varošanec, S., Multidimensional and discrete Steffensen's inequality, Southeast Asian Bulletin of Mathematics, 23, pp. 277-284, 1999.

Steffensen, J. F., On certain inequalities and methods of approximation, J. Institute Actuaries, 51, pp. 274-297, 1919, https://doi.org/10.1017/S0020268100028687. DOI: https://doi.org/10.1017/S0020268100028687

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Published

2003-02-01

How to Cite

Pečarić, J., & Varošanec, S. (2003). On convexity-like inequalities (II). Rev. Anal. Numér. Théor. Approx., 32(1), 79–84. https://doi.org/10.33993/jnaat321-737

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