A note on characterization of $h$-convex functions via Hermite--Hadamard type inequality
Problemy analiza, Tome 8 (2019) no. 2, pp. 28-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

A characterization of $h$-convex function via Hermite–Hadamard inequality related to the $h$-convex functions is investigated. In fact it is determined that under what conditions a function is $h$-convex, if it satisfies the $h$-convex version of Hermite–Hadamard inequality.
Keywords: $h$-convex function, Hermite–Hadamard inequality.
@article{PA_2019_8_2_a1,
     author = {M. Rostamian Delavar and S. S. Dragomir and M. De La Sen},
     title = {A note on characterization of $h$-convex functions via {Hermite--Hadamard} type inequality},
     journal = {Problemy analiza},
     pages = {28--36},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2019_8_2_a1/}
}
TY  - JOUR
AU  - M. Rostamian Delavar
AU  - S. S. Dragomir
AU  - M. De La Sen
TI  - A note on characterization of $h$-convex functions via Hermite--Hadamard type inequality
JO  - Problemy analiza
PY  - 2019
SP  - 28
EP  - 36
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2019_8_2_a1/
LA  - en
ID  - PA_2019_8_2_a1
ER  - 
%0 Journal Article
%A M. Rostamian Delavar
%A S. S. Dragomir
%A M. De La Sen
%T A note on characterization of $h$-convex functions via Hermite--Hadamard type inequality
%J Problemy analiza
%D 2019
%P 28-36
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2019_8_2_a1/
%G en
%F PA_2019_8_2_a1
M. Rostamian Delavar; S. S. Dragomir; M. De La Sen. A note on characterization of $h$-convex functions via Hermite--Hadamard type inequality. Problemy analiza, Tome 8 (2019) no. 2, pp. 28-36. http://geodesic.mathdoc.fr/item/PA_2019_8_2_a1/

[1] Breckner W. W., “Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen”, Publ. Inst. Math., 23 (1978), 13–20 | MR | Zbl

[2] Dragomir S. S., Pečarić J., Persson L. E., “Some inequalities of Hadamard type”, Soochow J. Math., 21 (1995), 335–341 | MR | Zbl

[3] Godunova E. K., Levin V. I., “Neravenstva dlja funkcii širokogo klassa, soderžaščego vypuklye, monotonnye i nekotorye drugie vidy funkcii”, Vyčislitel. Mat. i. Mat. Fiz. Mežvuzov, Sb. Nauč. Trudov, MGPI, M., 1985, 138–142

[4] Házy A., “Bernstein-Doetsch type results for $h$-convex functions”, Math. Ineq. Appl., 14:3 (2011), 499–508 | DOI | MR | Zbl

[5] Niculescu C. P., Persson L. E., Convex functions and their applications: a contemporary approach, CMS Books in Mathematics, Springer, Berlin, 2006 | DOI | MR | Zbl

[6] Robert A. W., Varbeg D. E., Convex functions, Academic Press, New York, 1973 | MR | Zbl

[7] Rudin W., Principles of mathematical analysis, McGraw-Hill, 1976 | MR | Zbl

[8] Sarikaya M. Z., Saglam A., Yildirim H., “On Some Hadamard-Type Inequalities for $h$-Convex Functions”, J. Math. Ineq., 2:3 (2008), 335–341 | DOI | MR | Zbl

[9] Varošanec S., “On $h$-convexity”, J. Math. Anal. Appl., 326 (2007), 303–311 | DOI | MR | Zbl