Inequalities of Hermite--Hadamard type for $HG$-convex functions
Problemy analiza, Tome 6 (2017) no. 2, pp. 25-41.

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

Some inequalities of Hermite-Hadamard type for $HG$-convex functions defined on positive intervals are given. Applications for special means are also provided.
Keywords: convex functions, integral inequalities, $HG$-convex functions.
@article{PA_2017_6_2_a1,
     author = {S. S. Dragomir},
     title = {Inequalities of {Hermite--Hadamard} type for $HG$-convex functions},
     journal = {Problemy analiza},
     pages = {25--41},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2017_6_2_a1/}
}
TY  - JOUR
AU  - S. S. Dragomir
TI  - Inequalities of Hermite--Hadamard type for $HG$-convex functions
JO  - Problemy analiza
PY  - 2017
SP  - 25
EP  - 41
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2017_6_2_a1/
LA  - en
ID  - PA_2017_6_2_a1
ER  - 
%0 Journal Article
%A S. S. Dragomir
%T Inequalities of Hermite--Hadamard type for $HG$-convex functions
%J Problemy analiza
%D 2017
%P 25-41
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2017_6_2_a1/
%G en
%F PA_2017_6_2_a1
S. S. Dragomir. Inequalities of Hermite--Hadamard type for $HG$-convex functions. Problemy analiza, Tome 6 (2017) no. 2, pp. 25-41. http://geodesic.mathdoc.fr/item/PA_2017_6_2_a1/

[1] Alomari M., Darus M., “The Hadamard's inequality for s-convex function”, Int. J. Math. Anal., 2:13 (2008), 639–646 | MR | Zbl

[2] Alomari M., Darus M., “Hadamard-type inequalities for s-convex functions”, Int. Math. Forum, 3:37 (2008), 1965–1975 | MR | Zbl

[3] Anastassiou G. A., “Univariate Ostrowski inequalities, revisited”, Monatsh. Math., 135:3 (2002), 175–189 | DOI | MR | Zbl

[4] Anderson G. D., Vamanamurthy M. K., Vuorinen M., “Generalized convexity and inequalities”, J. Math. Anal. Appl., 335 (2007), 1294–1308 | DOI | MR | Zbl

[5] Barnett N. S., Cerone P., Dragomir S. S., Pinheiro M. R., Sofo A., “Ostrowski type inequalities for functions whose modulus of the derivatives are convex and applications”, Inequality Theory and Applications (Chinju/Masan, 2001), v. 2, Nova Sci. Publ., Hauppauge, NY, 19–32 ; RGMIA Res. Rep. Coll., 5:2 (2003), 1 http://rgmia.org/papers/v5n2/Paperwapp2q.pdf | MR | Zbl

[6] Beckenbach E. F., “Convex functions”, Bull. Amer. Math. Soc., 54 (1948), 439–460 | DOI | MR | Zbl

[7] Bombardelli M., Varošanec S., “Properties of $h$-convex functions related to the Hermite-Hadamard-Fejér inequalities”, Comput. Math. Appl., 58:9 (2009), 1869–1877 | DOI | MR | Zbl

[8] Cristescu G., “Hadamard type inequalities for convolution of $h$-convex functions”, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 8 (2010), 3–11 | MR | Zbl

[9] Dragomir S. S., “On the Ostrowski's inequality for mappings of bounded variation and applications”, Math. Ineq. Appl., 4:1 (2001), 33–40 | MR

[10] Dragomir S. S., “An inequality improving the first Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products”, J. Inequal. Pure Appl. Math., 3:2 (2002), 31, 8 pp. | MR | Zbl

[11] Dragomir S. S., “An inequality improving the second Hermite–Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products”, J. Inequal. Pure Appl. Math., 3:3 (2002), 35 | MR

[12] Dragomir S. S., “An Ostrowski like inequality for convex functions and applications”, Revista Math. Complutense, 16:2 (2003), 373–382 | MR | Zbl

[13] Dragomir S. S., Operator Inequalities of Ostrowski and Trapezoidal Type, Springer Briefs in Mathematics, Springer, New York, 2012, x+112 pp. | MR | Zbl

[14] Dragomir S. S., “Some new inequalities of Hermite–Hadamard type for GA-convex functions”, Preprint RGMIA Res. Rep. Coll., 18 (2015), 30 http://rgmia.org/papers/v18/v18a30.pdf | MR

[15] Dragomir S. S., “Inequalities of Hermite–Hadamard type for HA-convex functions”, Preprint RGMIA Res. Rep. Coll., 18 (2015), 38 http://rgmia.org/papers/v18/v18a38.pdf | MR

[16] Dragomir S. S., “New inequalities of Hermite–Hadamard type for HAconvex functions”, Preprint RGMIA Res. Rep. Coll., 18 (2015), 41 http://rgmia.org/papers/v18/v18a41.pdf

[17] Dragomir S. S., Cerone P., Roumeliotis J., Wang S., “A weighted version of Ostrowski inequality for mappings of Hölder type and applications in numerical analysis”, Bull. Math. Soc. Sci. Math. Romanie, 42(90):4 (1999), 301–314 | MR | Zbl

[18] Dragomir S. S., Fitzpatrick S., “The Hadamard inequalities for $s$-convex functions in the second sense”, Demonstratio Math., 32:4 (1999), 687–696 | MR | Zbl

[19] Dragomir S. S., Fitzpatrick S., “The Jensen inequality for $s$-Breckner convex functions in linear spaces”, Demonstratio Math., 33:1 (2000), 43–49 | MR | Zbl

[20] Dragomir S. S., Mond B., “On Hadamard's inequality for a class of functions of Godunova and Levin”, Indian J. Math., 39:1 (1997), 1–9 | MR | Zbl

[21] Dragomir S. S., Pearce C. E. M., “On Jensen's inequality for a class of functions of Godunova and Levin”, Period. Math. Hungar., 33:2 (1996), 93–100 | DOI | MR | Zbl

[22] Dragomir S. S., Pearce C. E. M., “Quasi-convex functions and Hadamard's inequality”, Bull. Austral. Math. Soc., 57 (1998), 377–385 | DOI | MR | Zbl

[23] Dragomir S. S., Pečarić J., Persson L.-E., “Some inequalities of Hadamard type”, Soochow J. Math., 21:3 (1995), 335–341 | MR | Zbl

[24] Dragomir S. S., Rassias Th. M. (eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publisher, 2002 | MR | Zbl

[25] El Farissi A., “Simple proof and refinement of Hermite–Hadamard inequality”, J. Math. Ineq., 4:3 (2010), 365–369 | DOI | MR | Zbl

[26] Işcan I., “Hermite–Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, 43:6 (2014), 935–942 | MR

[27] Kikianty E., Dragomir S. S., “Hermite–Hadamard's inequality and the pHH-norm on the Cartesian product of two copies of a normed space”, Math. Inequal. Appl., 13:1 (2010), 1–32 | MR | Zbl

[28] Pečarić J. E., Dragomir S. S., “On an inequality of Godunova–Levin and some refinements of Jensen integral inequality”, Itinerant Seminar on Functional Equations, Approximation and Convexity, Preprint 89-6 (Cluj-Napoca, 1989), Univ. "Babeş-Bolyai", Cluj-Napoca, 1989, 263–268 | MR