On convexity-like inequalities (II)
DOI:
https://doi.org/10.33993/jnaat321-737Keywords:
Jensen's inequality, convexity-like inequalities, generalized Steffensen's inequalityAbstract
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.Downloads
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
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.