×

On further refinements of the Jensen inequality and applications. (English) Zbl 07869422

MSC:

26A51 Convexity of real functions in one variable, generalizations
26D15 Inequalities for sums, series and integrals
Full Text: DOI

References:

[1] S.Furuichi and H. R.Moradi, Advances in mathematical inequalities, De Gruyter, 2020. · Zbl 1447.26017
[2] D. S.Mitrinović, J. E.Pečarić, and A. M.Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht/Boston/London, 1993. · Zbl 0771.26009
[3] C. P.Niculescu and L. E.Persson, Convex functions and their applications. A contemporary approach, CMS Books in Mathematics, Vol. 23, Springer-Verlag, New York, 2006. · Zbl 1100.26002
[4] J. E.Pečarić, F.Proschan, and Y. L.Tong, Convex functions, partial orderings, and statistical applications, Academic Press, Inc, 1992. · Zbl 0749.26004
[5] S. S.Dragomir, J. E.Pečarić, and L. E.Persson, Properties of some functionals related to Jensen’s inequality, Acta Math. Hungar.70 (1996), no. 1-2, 129-143. · Zbl 0847.26013
[6] M.Krnić, N.Lovričević, and J.Pečarić, Jessen’s functional, its properties and applications, An. Şt. Univ Ovidius Constanţa20 (2012), 225-248. · Zbl 1274.26058
[7] M.Krnić, N.Lovričević, and J.Pečarić, On the properties of McShane’s functional and their applications, Period Math. Hung.66 (2013), 159-180. · Zbl 1299.26045
[8] F. C.Mitroi, About the precision in Jensen‐Steffensen inequality, Ann. Univ. Craiova Math. Comput. Sci. Ser.37 (2010), 73-84. · Zbl 1224.26045
[9] M.Krnić, N.Lovričević, J.Pečarić, and J.Perić, Superadditivity and monotonicity of the Jensen‐type functionals, Element, Zagreb, 2015.
[10] S. S.Dragomir, Bounds for the normalized Jensen’s functional, Bull. Austral. Math. Soc.74 (2006), 471-478. · Zbl 1113.26021
[11] S.Varošanec, On
[( h \]\)‐convexity, J. Math. Anal. Appl.326 (2007), 303-311. · Zbl 1111.26015
[12] M. B.Khan, H. M.Srivastava, P. O.Mohammed, K.Nonlaopon, and Y. S.Hamed, Some new Jensen, Schur and Hermite‐Hadamard inequalities for log convex fuzzy interval‐valued functions, AIMS Math.7 (2022), 4338-4358.
[13] H. M.Srivastava, Z.‐H.Zhang, and Y.‐D.Wu, Some further refinements and extensions of the Hermite‐Hadamard and Jensen inequalities in several variables, Math. Comput. Model.54 (2011), 2709-2717. · Zbl 1235.26016
[14] Z.‐G.Xiao, H. M.Srivastava, and Z.‐H.Zhang, Further refinements of the Jensen inequalities based upon samples with repetitions, Math. Comput. Model.51 (2010), 592-600. · Zbl 1190.26031
[15] I.Perić, On boundary domination in the Jensen-Mercer inequality, J. Math. Ineqal.9 (2015), no. 4, 983-1000. · Zbl 1333.26013
[16] I.Csiszár, Information‐type measures of differences of probability distributions and indirect observations, Studia Sci. Math. Hungar.2 (1967), 299-318. · Zbl 0157.25802
[17] S. S.Dragomir, Superadditivity of some functionals associated with Jensen’s inequality for convex functions on linear spaces with applications, Bull. Aust. Math. Soc.82 (2010), no. 3, 44-61. · Zbl 1204.26033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.