zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Refinements of the lower bounds of the Jensen functional. (English) Zbl 1225.26041
Summary: The lower bounds of the functional defined as the difference of the right-hand and the left-hand side of the Jensen inequality are studied. Refinements of some previously known results are given by applying results from the theory of majorization. Furthermore, some interesting special cases are considered.

26D15Inequalities for sums, series and integrals of real functions
Full Text: DOI
[1] D. S. Mitrinović, J. E. Pe\vcarić, and A. M. Fink, Classical and New Inequalities in Analysis, vol. 61 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993. · Zbl 0771.26009
[2] J. L. W. V. Jensen, “Sur les fonctions convexes et les inégalités entre les valeurs moyennes,” Acta Mathematica, vol. 30, no. 1, pp. 175-193, 1906. · Zbl 37.0422.02 · doi:10.1007/BF02418571
[3] S. S. Dragomir, J. Pe\vcarić, and L. E. Persson, “Properties of some functionals related to Jensen’s inequality,” Acta Mathematica Hungarica, vol. 70, no. 1-2, pp. 129-143, 1996. · Zbl 0847.26013 · doi:10.1007/BF00113918
[4] S. S. Dragomir, “Bounds for the normalised Jensen functional,” Bulletin of the Australian Mathematical Society, vol. 74, no. 3, pp. 471-478, 2006. · Zbl 1113.26021 · doi:10.1017/S000497270004051X
[5] J. Barić, M. Matić, and J. E. Pe\vcarić, “On the bounds for the normalized Jensen functional and Jensen-Steffensen inequality,” Mathematical Inequalities & Applications, vol. 12, no. 2, pp. 413-432, 2009. · Zbl 1168.26002 · http://files.ele-math.com/abstracts/mia-12-32-abs.pdf
[6] S. Abramovich, S. Ivelić, and J. E. Pe\vcarić, “Improvement of Jensen-Steffensen’s inequality for superquadratic functions,” Banach Journal of Mathematical Analysis, vol. 4, no. 1, pp. 159-169, 2010. · Zbl 1195.26037 · emis:journals/BJMA/tex_v4_n1_a12.pdf · eudml:226463
[7] S. Ivelić, A. Matković, and J. E. Pe\vcarić, “On a Jensen-Mercer operator inequality,” Banach Journal of Mathematical Analysis, vol. 5, no. 1, pp. 19-28, 2011. · Zbl 1221.47031 · emis:journals/BJMA/tex_v5_n1_a2.pdf
[8] M. Khosravi, J. S. Aujla, S. S. Dragomir, and M. S. Moslehian, “Refinements of Choi-Davis-Jensen’s inequality,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 2, pp. 127-133, 2011. · Zbl 1314.47022
[9] V. Cirtoaje, “The best lower bound depended on two fixed variables for Jensen’s inequality with ordered variables,” Journal of Inequalities and Applications, vol. 2010, Article ID 128258, 12 pages, 2010. · Zbl 1204.26031 · doi:10.1155/2010/128258 · eudml:222792
[10] N. Latif, J. Pe\vcarić, and I. Perić, “On majorization of vectors, Favard and Berwald inequalities,” In press.