×

Refinements of the Hermite-Hadamard inequality in NPC global spaces. (English) Zbl 1401.39028

Summary: In this paper we establish different refinements and applications of the Hermite-Hadamard inequality for convex functions in the context of NPC global spaces.

MSC:

39B62 Functional inequalities, including subadditivity, convexity, etc.
32F17 Other notions of convexity in relation to several complex variables
26E60 Means
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abramovich S., Baric J., Pecaric J., Fejer and Hermite-Hadamard type inequalities for superquadratic functions, J. Math. Anal. Appl. 344 (2008), no. 2, 1048-1056. · Zbl 1141.26006
[2] Barnett N.S., Cerone P., Dragomir S.S., Some new inequalities for Hermite-Hadamard divergence in information theory, Stochastic analysis and applications Vol. 3, 7-19, Nova Sci. Publ., Hauppauge, New York, 2003.
[3] Bessenyei M., Hermite-Hadamard-type inequalities for generalized convex functions, J. Inequal. Pure Appl. Math. 9 (2008), no. 3, Art. 63, 51 pp. · Zbl 1173.26007
[4] Bhatia R., The logarithmic mean, Resonance 13 (2008), no. 6, 583-594.
[5] Carlson B.C., The logarithmic mean, Amer. Math. Monthly 79 (1972), no. 6, 615-618. · Zbl 0241.33001
[6] Cerone P., Dragomir S.S., Mathematical inequalities. A perspective, CRC Press, Boca Raton, 2011.
[7] Conde C., A version of the Hermite-Hadamard inequality in a nonpositive curvature space, Banach J. Math. Anal. 6 (2012), no. 2, 159-167. · Zbl 1247.39026
[8] Dragomir S.S., Bounds for the normalised Jensen functional, Bull. Austral. Math. Soc. 74 (2006), no. 3, 471-478. · Zbl 1113.26021
[9] Dragomir S.S., Hermite-Hadamard’s type inequalities for operator convex functions, Appl. Math. Comput. 218 (2011), no. 3, 766-772. · Zbl 1239.47009
[10] Dragomir S.S., Pearce C.E.M., Selected Topics on Hermite-Hadamard Inequalities, RGMIA Monographs, Victoria University, 2000. Available at http://rgmia.vu.edu.au/monographs/hermite_hadamard.html
[11] El Farissi A., Simple proof and refinement of Hermite-Hadamard inequality. J. Math. Inequal. 4 (2010), no. 3, 365-369. · Zbl 1197.26017
[12] Hadamard J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann (French), J. Math. Pures et Appl. 58 (1893), 171-215.
[13] Házy A., Páles Z., On a certain stability of the Hermite-Hadamard inequality, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009), no. 2102, 571-583. · Zbl 1186.39032
[14] Jost J., Nonpositive curvature: geometric and analytic aspects, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1997. · Zbl 0896.53002
[15] Kikianty E., Hermite-Hadamard inequality in the geometry of Banach spaces, PhD thesis, Victoria University, 2010. Available at eprints.vu.edu.au/15793/1/ EderKikiantyThesis.pdf.
[16] Klaricic M., Neuman E., Pecaric J., Šimic V., Hermite-Hadamard’s inequalities for multivariate g-convex functions, Math. Inequal. Appl. 8 (2005), no. 2, 305-316. · Zbl 1071.26015
[17] Lang S., Fundamentals of differential geometry, Graduate Texts in Mathematics, Springer-Verlag, New York, 1999. · Zbl 0932.53001
[18] Leach E.B., Sholander M.C., Extended mean values. II, J. Math. Anal. Appl. 92 (1983), no. 1, 207-223. · Zbl 0517.26007
[19] Mihailescu M., Niculescu C.P., An extension of the Hermite-Hadamard inequality through subharmonic functions, Glasg. Math. J. 49 (2007), no. 3, 509-514. · Zbl 1136.35022
[20] Mitroi F.-C., About the precision in Jensen-Steffensen inequality, An. Univ. Craiova Ser. Mat. Inform. 37 (2010), no. 4, 73-84. · Zbl 1224.26045
[21] Niculescu C.P., Persson L.-E., Convex functions and their applications. A contemporary approach, Springer, New York, 2006. · Zbl 1100.26002
[22] Wu S., On the weighted generalization of the Hermite-Hadamard inequality and its applications, Rocky Mountain J. Math. 39 (2009), no. 5, 1741-1749. · Zbl 1181.26042
[23] Zabandan G., A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10 (2009), no. 2, Art. 45, 7 pp. · Zbl 1168.26320
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.