Inequalities of Jensen type for \(AH\)-convex functions
DOI:
https://doi.org/10.33993/jnaat452-1085Keywords:
Convex functions, Integral inequalities, AH-Convex functions.Abstract
Some integral inequalities of Jensen type for AH-convex functions defined on intervals of real line are given.
Applications for power and logarithm functions are provided as well. Some inequalities for functions of selfadjoint operators in Hilbert spaces are also established.
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S. Abramovich, Convexity, subadditivity and generalized Jensen’s inequality. Ann. Funct. Anal. 4 (2013), no. 2, 183-194, http://dx.doi.org/10.15352/afa/1399899535 DOI: https://doi.org/10.15352/afa/1399899535
J. M. Aldaz, A measure-theoretic version of the Dragomir-Jensen inequality. Proc. Amer. Math. Soc. 140 (2012), no. 7, 2391-2399, http://dx.doi.org/10.1090/s0002-9939-2011-11088-8 DOI: https://doi.org/10.1090/S0002-9939-2011-11088-8
V. Cirtoaje, The best lower bound for Jensen’s inequality with three fixed ordered variables. Banach J. Math. Anal. 7 (2013), no. 1, 116-131, http://dx.doi.org/10.15352/bjma/1358864553 DOI: https://doi.org/10.15352/bjma/1358864553
S. S. Dragomir, A converse result for Jensen’s discrete inequality via Gruss’ inequality and applications in information theory. An. Univ. Oradea Fasc. Mat. 7 (1999/2000), 178-189.
S. S. Dragomir, On a reverse of Jessen’s inequality for isotonic linear functionals, J. Ineq. Pure & Appl. Math., 2 (2001), No. 3, Article 36.
S. S. Dragomir, A Gruss type inequality for isotonic linear functionals and applications. Demonstratio Math. 36 (2003), no. 3, 551–562. Preprint RGMIA Res. Rep. Coll. 5 (2002), Suplement, Art. 12, http://rgmia.org/v5(E).php DOI: https://doi.org/10.1515/dema-2003-0308
S. S. Dragomir, Bounds for the deviation of a function from the chord generated by its extremities. Bull. Aust. Math. Soc. 78 (2008), no. 2, 225-248, http://dx.doi.org/10.1017/s0004972708000671 DOI: https://doi.org/10.1017/S0004972708000671
S. S. Dragomir, Bounds for the normalized Jensen functional. Bull. Austral. Math. Soc. 74 (3) (2006), 471-476. DOI: https://doi.org/10.1017/S000497270004051X
S. S. Dragomir, Reverses of the Jensen inequality in terms of first derivative and applications. Acta Math. Vietnam. 38 (2013), no. 3, 429-446, http://dx.doi.org/10.1007/s40306-013-0029-9 DOI: https://doi.org/10.1007/s40306-013-0029-9
S. S. Dragomir, Some reverses of the Jensen inequality with applications. Bull. Aust. Math. Soc. 87 (2013), no. 2, 177-194, http://dx.doi.org/10.1017/s0004972712001098 DOI: https://doi.org/10.1017/S0004972712001098
S. S. Dragomir, A refinement and a divided difference reverse of Jensen’s inequality with applications, accepted Rev. Colomb. Mate., Preprint RGMIA Res. Rep Coll. 14 (2011), Art 74, http://rgmia.org/papers/v14/v14a74.pdf
S. S. Dragomir and N. M. Ionescu, Some converse of Jensen’s inequality and applications. Rev. Anal. Numer. Theor. Approx. 23 (1994), no. 1, 71-78, http://ictp.acad.ro/jnaat/journal/article/view/1994-vol23-no1-art7
G. Helmberg, Introduction to Spectral Theory in Hilbert Space, John Wiley, New York, 1969.
L. Horvath, A new refinement of discrete Jensen’s inequality depending on parameters. J. Inequal. Appl. 2013 , 2013:551, 16 pp., http://dx.doi.org/10.1186/1029-242x-2013-551 DOI: https://doi.org/10.1186/1029-242X-2013-551
K. M. Adil, S. Khalid and J. Pecaric, Improvement of Jensen’s inequality in terms of Gateaux derivatives for convex functions in linear spaces with applications. Kyungpook Math. J. 52 (2012), no. 4, 495–511, http://dx.doi.org/10.5666/kmj.2012.52.4.495 DOI: https://doi.org/10.5666/KMJ.2012.52.4.495
M. V. Mihai, Jensen’s inequality for fixed convex functions of two real variables. Acta Univ. Apulensis Math. Inform. No. 34 (2013), 179-183.
M. Kian, Operator Jensen inequality for superquadratic functions. Linear Algebra Appl. 456 (2014), 82-87, http://dx.doi.org/10.1016/j.laa.2012.12.011 DOI: https://doi.org/10.1016/j.laa.2012.12.011
C. P. Niculescu, An extension of Chebyshev’s inequality and its connection with Jensen’s inequality. J. Inequal. Appl. 6 (2001), no. 4, 451-462, http://dx.doi.org/10.1155/s1025583401000273 DOI: https://doi.org/10.1155/S1025583401000273
Z. Pavic, The applications of functional variants of Jensen’s inequality. J. Funct. Spaces Appl. 2013 , Art. ID 194830, 5 pp., http://dx.doi.org/10.1155/2013/194830 DOI: https://doi.org/10.1155/2013/194830
F. Popovici and C.-I. Spiridon, The Jensen inequality for (M, N)-convex functions. An. Univ. Craiova Ser. Mat. Inform. 38 (2011), no. 4, 63-66.
R. Sharma, On Jensen’s inequality for positive linear functionals. Int. J. Math. Sci. Eng. Appl. 5 (2011), no. 5, 263-271.
S. Simic, On a global upper bound for Jensen’s inequality, J. Math. Anal. Appl. 343 (2008), 414-419, http://dx.doi.org/10.1016/j.jmaa.2008.01.060 DOI: https://doi.org/10.1016/j.jmaa.2008.01.060
G. Zabandan and A. Kilicman, A new version of Jensen’s inequality and related results. J. Inequal. Appl. 2012 , 2012:238, 7 pp., http://dx.doi.org/10.1186/1029-242x-2012-238 DOI: https://doi.org/10.1186/1029-242X-2012-238
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