On a mean value theorem connected with Hermite-Hadamard's inequality

Authors

  • Ovidiu T. Pop “Mihai Eminescu” National College, Satu Mare, Romania

DOI:

https://doi.org/10.33993/jnaat332-780

Keywords:

convex function, mean-value theorem, intermediate point
Abstract views: 218

Abstract

In this paper we prove a mean-value theorem for integral calculus, then we demonstrate properties of the mean point. In the end we give an extension of Hermite-Hadamard's inequality.

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References

Beckenbach, E.F. and Bellman, R., Inequalities, Springer-Verlag, Berlin-Götingen-Heidelberg, 1961. DOI: https://doi.org/10.1007/978-3-642-64971-4

Berinde, V., Despre proprietatea punctului intermediar în teoremele de medie pentru integrala Riemann, Lucrările Seminarului de Creativitate Matematică, Universitatea de Nord Baia Mare, 9, pp. 51-58, 2000 (in Romanian).

Florea, A. and Niculescu, C.P., Extensii ale inegalităţii Hermite-Hadamard, Lucrările Seminarului de Creativitate Matematică, Universitatea de Nord Baia Mare, 10, pp. 97-106, 2001 (in Romanian).

Hadamard, J., Étude sur les propriétés des functions entières et en particulier d'une function considérée par Riemann, J. Math. Pures Appl., 58, pp. 171-215, 1893.

Hardy, G. H., Littlewood, J. E. and Pólya, G., Inequalities, Cambridge University Press, 1934.

Jacobson, B., On the mean value theorem for integrals, Amer. Math. Monthly, 89, pp. 300--301, 1982, https://doi.org/10.1080/00029890.1982.11995437. DOI: https://doi.org/10.1080/00029890.1982.11995437

Mitrinovič, D. S., Analytic inequalities, Springer Berlin-Heidelberg-New York, 1970.

Mitrinovič, D. S. and Lackovič, I. B., Hermite and converxity, Aequationes Mathematicae, 28, pp. 229-232, 1985, https://doi.org/10.1007/BF02189414. DOI: https://doi.org/10.1007/BF02189414

Nicolescu, M., Mathematical Analysis, II, Editura Tehnică, Bucureşti, 1958 (in Romanian).

Niculescu, C. P., Asupra inegalităţilor de convexitate in absenţa derivabilităţii, Gazeta Matematică, CIII, no. 9, pp. 329-337, 1998 (in Romanian).

Pop, I., O caracterizare a funcţiilor convexe, Gazeta matematică, IC, no.7, pp. 313-314, 1994 (in Romanian).

Rockafellar, R.T., Convex analysis, Princeton University Press, 1970. DOI: https://doi.org/10.1515/9781400873173

Sireţchi, Gh., Calcul diferenţial şi integral, Editura Ştiinţifică şi Enciclopedică, Bucureşti, I, 1985 (in Romanian).

Udrişte, C., Tănăsescu, E., Minime şi maxime ale funcţiilor reale de variabile reale, Editura Tehnică, Bucureşti, 1980 (in Romanian).

Zhang Bao-lin, A note on the mean value theorem for integrals, Amer. Math. Monthly 104, pp. 561-562, 1997, https://doi.org/10.1080/00029890.1997.11990679. DOI: https://doi.org/10.1080/00029890.1997.11990679

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Published

2004-08-01

How to Cite

Pop, O. T. (2004). On a mean value theorem connected with Hermite-Hadamard’s inequality. Rev. Anal. Numér. Théor. Approx., 33(2), 221–228. https://doi.org/10.33993/jnaat332-780

Issue

Vol. 33 No. 2 (2004)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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