AN EXTENSION OF THE HERMITE-HADAMARD INEQUALITY THROUGH SUBHARMONIC FUNCTIONS*
Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 509-514

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we obtain a Hermite-Hadamard type inequality for a class of subharmonic functions. Our proofs rely essentially on the properties of elliptic partial differential equations of second order. Our study extends some recent results from [1], [2] and [6].
DOI : 10.1017/S0017089507003837
Mots-clés : 35R45, 35J15, 35J60.
MIHĂILESCU, MIHAI; NICULESCU, CONSTANTIN P. AN EXTENSION OF THE HERMITE-HADAMARD INEQUALITY THROUGH SUBHARMONIC FUNCTIONS*. Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 509-514. doi: 10.1017/S0017089507003837
@article{10_1017_S0017089507003837,
     author = {MIH\u{A}ILESCU, MIHAI and NICULESCU, CONSTANTIN P.},
     title = {AN {EXTENSION} {OF} {THE} {HERMITE-HADAMARD} {INEQUALITY} {THROUGH} {SUBHARMONIC} {FUNCTIONS*}},
     journal = {Glasgow mathematical journal},
     pages = {509--514},
     year = {2007},
     volume = {49},
     number = {3},
     doi = {10.1017/S0017089507003837},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003837/}
}
TY  - JOUR
AU  - MIHĂILESCU, MIHAI
AU  - NICULESCU, CONSTANTIN P.
TI  - AN EXTENSION OF THE HERMITE-HADAMARD INEQUALITY THROUGH SUBHARMONIC FUNCTIONS*
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 509
EP  - 514
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003837/
DO  - 10.1017/S0017089507003837
ID  - 10_1017_S0017089507003837
ER  - 
%0 Journal Article
%A MIHĂILESCU, MIHAI
%A NICULESCU, CONSTANTIN P.
%T AN EXTENSION OF THE HERMITE-HADAMARD INEQUALITY THROUGH SUBHARMONIC FUNCTIONS*
%J Glasgow mathematical journal
%D 2007
%P 509-514
%V 49
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003837/
%R 10.1017/S0017089507003837
%F 10_1017_S0017089507003837

[1] 1.Fink, A. M., A best possible Hadamard inequality, Math. Inequal. Appl., 1 (1998), 223–230. Google Scholar

[2] 2.Florea, A. and Niculescu, C. P., A Hermite-Hadamard inequality for convex-concave symmetric functions, Bull. Soc. Sci. Math. Roum., 50 (98) (2007), No. 2. Google Scholar

[3] 3.Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order (Springer-Verlag, 1998). Google Scholar

[4] 4.Jost, J., Partial differential equations (Springer-Verlag, 2000). Google Scholar

[5] 5.Montel, P., Sur les fonctions convexes et les fonctions sousharmonique, Journal de Math., (), 7 (1928), 29–60. Google Scholar

[6] 6.Niculescu, C. P. and Persson, L.-E., Old and new on the Hermite-Hadamard inequality, Real Anal. Exchange, 29 (2003/2004), 663–686. Google Scholar | DOI

[7] 7.Niculescu, C. P. and Persson, L.-E., Convex functions and their applications. A contemporary approach, CMS Books in Mathematics vol. 23 (Springer-Verlag, 2006). Google Scholar | DOI

[8] 8.Ockendon, J., Howison, S., Lacey, A. and Movchan, A., Applied partial differential equations (Oxford University Press, 2003). Google Scholar | DOI

[9] 9.Proter, M. H. and Weinberger, H. F., Maximum principles in differential equations (Springer-Verlag, 1984). Google Scholar | DOI

Cité par Sources :