Jensen's inequality (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Jensen's inequality" in English language version.

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Gao, Xiang; Sitharam, Meera; Roitberg, Adrian (2019). "Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions" (PDF). The Australian Journal of Mathematical Analysis and Applications. 16 (2). arXiv:1712.05267.

ams.org

mathscinet.ams.org

Guessab, A.; Schmeisser, G. (2013). "Necessary and sufficient conditions for the validity of Jensen's inequality". Archiv der Mathematik. 100 (6): 561–570. doi:10.1007/s00013-013-0522-3. MR 3069109. S2CID 56372266.

arxiv.org

Gao, Xiang; Sitharam, Meera; Roitberg, Adrian (2019). "Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions" (PDF). The Australian Journal of Mathematical Analysis and Applications. 16 (2). arXiv:1712.05267.
Liao, J.; Berg, A (2018). "Sharpening Jensen's Inequality". American Statistician. 73 (3): 278–281. arXiv:1707.08644. doi:10.1080/00031305.2017.1419145. S2CID 88515366.

doi.org

Jensen, J. L. W. V. (1906). "Sur les fonctions convexes et les inégalités entre les valeurs moyennes". Acta Mathematica. 30 (1): 175–193. doi:10.1007/BF02418571.
Guessab, A.; Schmeisser, G. (2013). "Necessary and sufficient conditions for the validity of Jensen's inequality". Archiv der Mathematik. 100 (6): 561–570. doi:10.1007/s00013-013-0522-3. MR 3069109. S2CID 56372266.
Dekking, F.M.; Kraaikamp, C.; Lopuhaa, H.P.; Meester, L.E. (2005). A Modern Introduction to Probability and Statistics: Understanding Why and How. Springer Texts in Statistics. London: Springer. doi:10.1007/1-84628-168-7. ISBN 978-1-85233-896-1.
Attention: In this generality additional assumptions on the convex function and/ or the topological vector space are needed, see Example (1.3) on p. 53 in Perlman, Michael D. (1974). "Jensen's Inequality for a Convex Vector-Valued Function on an Infinite-Dimensional Space". Journal of Multivariate Analysis. 4 (1): 52–65. doi:10.1016/0047-259X(74)90005-0. hdl:11299/199167.
Liao, J.; Berg, A (2018). "Sharpening Jensen's Inequality". American Statistician. 73 (3): 278–281. arXiv:1707.08644. doi:10.1080/00031305.2017.1419145. S2CID 88515366.

duke.edu

services.math.duke.edu

p. 25 of Rick Durrett (2019). Probability: Theory and Examples (5th ed.). Cambridge University Press. ISBN 978-1108473682.
p. 29 of Rick Durrett (2019). Probability: Theory and Examples (5th ed.). Cambridge University Press. ISBN 978-1108473682.

handle.net

hdl.handle.net

Attention: In this generality additional assumptions on the convex function and/ or the topological vector space are needed, see Example (1.3) on p. 53 in Perlman, Michael D. (1974). "Jensen's Inequality for a Convex Vector-Valued Function on an Infinite-Dimensional Space". Journal of Multivariate Analysis. 4 (1): 52–65. doi:10.1016/0047-259X(74)90005-0. hdl:11299/199167.

psu.edu

citeseerx.ist.psu.edu

Niculescu, Constantin P. "Integral inequalities", P. 12.

semanticscholar.org

api.semanticscholar.org

Guessab, A.; Schmeisser, G. (2013). "Necessary and sufficient conditions for the validity of Jensen's inequality". Archiv der Mathematik. 100 (6): 561–570. doi:10.1007/s00013-013-0522-3. MR 3069109. S2CID 56372266.
Liao, J.; Berg, A (2018). "Sharpening Jensen's Inequality". American Statistician. 73 (3): 278–281. arXiv:1707.08644. doi:10.1080/00031305.2017.1419145. S2CID 88515366.

springer.com

link.springer.com

Dekking, F.M.; Kraaikamp, C.; Lopuhaa, H.P.; Meester, L.E. (2005). A Modern Introduction to Probability and Statistics: Understanding Why and How. Springer Texts in Statistics. London: Springer. doi:10.1007/1-84628-168-7. ISBN 978-1-85233-896-1.

ukmt.org.uk

Bradley, CJ (2006). Introduction to Inequalities. Leeds, United Kingdom: United Kingdom Mathematics Trust. p. 97. ISBN 978-1-906001-11-7.

zenodo.org

Jensen, J. L. W. V. (1906). "Sur les fonctions convexes et les inégalités entre les valeurs moyennes". Acta Mathematica. 30 (1): 175–193. doi:10.1007/BF02418571.