On convex functions and related inequalities

Parvaneh Vaziri, Hadi Khodabakhshian, Rahim Safshekan

Abstract


The main result of this paper is to give refinement and reverse the celebrated Jensen inequality. We directly apply our results to establish several weighted arithmetic-geometric mean inequality. We also present a stronger estimate for the first inequality in the Hermite-Hadamard inequality.


Full Text:

PDF

References


M.D. Choi, A Schwarz inequality for positive linear maps on C*-algebras, Illinois J. Math. 18 (1974), 565-574.

S.S. Dragomir and N.M. Ionescu, Some Converse of Jensen's inequality and applications, Anal. Num. Theor. Approx. (Cluj-Napoca) 23 (1994), 71-78.

S. Furuichi, H.R. Moradi, and A. Zardadi, Some new Karamata type inequalities and their applications to some entropies, Rep. Math. Phys. 84 (2019), no. 2, 201-214. DOI: 10.1016/S0034-4877(19)30083-7

J. Micic, H.R. Moradi, and S. Furuichi, Choi-Davis-Jensen's inequality without convexity, J. Math. Inequal. 12 (2018), no. 4, 1075-1085. DOI: 10.7153/jmi-2018-12-82

B. Mond and J. Pecaric, On Jensen's inequality for operator convex functions, Houston J. Math. 21 (1995), 739-753.

H.R. Moradi and S. Furuichi, Improvement and generalization of some Jensen-Mercer-type inequalities, J. Math. Inequal. 14 (2020), no. 2, 377-383.

H.R. Moradi, S. Furuichi, and M. Sababheh, Some operator inequalities via convexity, Linear Multilinear Algebra. DOI: 10.1080/03081087.2021.2006592

H.R. Moradi, S. Furuichi, F.C. Mitroi-Symeonidis, and R. Naseri, An extension of Jensen's operator inequality and its application to Young inequality, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 113 (2019), no. 2, 605-614. DOI: 10.1007/s13398-018-0499-7

L. Nasiri, A. Zardadi, and H.R. Moradi, Re_ning and reversing Jensen's inequality, Oper. Matrices. 16 (2022), no. 1, 19-27. DOI: 10.7153/oam-2022-16-03

M. Sababheh, S. Furuichi, and H.R. Moradi, Composite convex functions, J. Math. Inequal. 15 (2021), no. 3, 1267-1285. DOI: 10.7153/jmi-2021-15-85

M. Sababheh, H.R. Moradi, and S. Furuichi, Integrals refining convex inequalities, Bull. Malays. Math. Sci. Soc. 43 (2020), 2817-2833. DOI: 10.1007/s40840-019-00839-0




DOI: https://doi.org/10.52846/ami.v50i1.1631