Inequalities via generalized $h$-convex functions
Problemy analiza, Tome 7 (2018) no. 2, pp. 112-130.

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In the paper, we establish some new Hermite–Hadamard–Fejér type inequalities via generalized $h$-convex functions, Toader-like convex functions and their variant forms. Several special cases are also discussed. Results proved in this paper can be viewed as significant new contributions in this field.
Keywords: generalized convex functions, generalized $h$-convex functions, Hermite–Hadamard–Fejér type inequalities, Toader-like convex function.
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M. A. Noor; K. I. Noor; F. Safdar. Inequalities via generalized $h$-convex functions. Problemy analiza, Tome 7 (2018) no. 2, pp. 112-130. http://geodesic.mathdoc.fr/item/PA_2018_7_2_a7/

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

[2] Breckner W. W., “Stetigkeitsaussagen fiir eine Klasse verallgemeinerter convexer funktionen in topologischen linearen Raumen”, Publ. Inst. Math., 23, 1978, 13–20 | MR | Zbl

[3] Cristescu G., Lupsa L., Non-connected Convexities and Applications, Kluwer Academic Publishers, Dordrechet, Holland, 2002 | MR | Zbl

[4] Delavar M. R., Dragomir S. S., “On $\eta$-convexity”, Math. Inequal. Appl., 20:1 (2017), 203–216 | MR | Zbl

[5] Dragomir S. S., Mond B., “Integral inequalities of Hadamard type for log-convex functions”, Demonstration, 31 (1998), 354–364 | MR

[6] Dragomir S. S., Pearce C. E., Selected topics on Hermite-Hadamard inequalities and applications, Victoria University, Australia, 2000

[7] Godunova E. K., Levin V. I., “Neravenstva dlja funkcii sirokogo klassa soderzascego vypuklye monotonnye i nekotorye drugie vidy funkii”, Vycislitel. Mat. i Fiz., Mezvuzov. Sb. Nauc., MGPI, M., 1985, 138–142 (in Russian)

[8] Gordji M. E., Delavar M. R., De La Sen M., “On $\varphi$ convex functions”, J. Math. Inequal., 10:1 (2016), 73–183 | MR

[9] Gordji M. E., Delavar M. R., Dragomir S. S., “An inequality related to $\eta$-convex functions (II)”, Int. J. Nonl. Anal. Appl., 6:2 (2015), 27–33 | Zbl

[10] Hadamard J., “Etude sur les proprietes des fonctions entieres e.t en particulier dune fonction consideree par Riemann”, J. Math. Pure. Appl., 58 (1893), 171–215

[11] Hermite C., “Sur deux limites d'une integrale definie”, Mathesis, 3 (1883), 82

[12] Hyers D. H., Ulam S. M., “Approximately convex functions”, Proc. Amer. Math. Soc., 3 (1952), 821–828 | DOI | MR | Zbl

[13] Niculescu C. P., Persson L. E., Convex Functions and Their Applications, Springer-Verlag, New York, 2006 | MR | Zbl

[14] Noor M. A., “General variational inequalities”, Appl. Math. Letters, 1:1 (1988), 119–121 | DOI | MR

[15] Noor M. A., “Some developments in general variational inequalities”, Appl. Math. Comput., 152 (2004), 199–277 | MR | Zbl

[16] Noor M. A., “Extended general variational inequalities”, Appl. Math. Letters, 22:2 (2009), 182–186 | DOI | MR | Zbl

[17] Noor M. A., Noor K. I., “Harmonic variational inequalities”, Appl. Math. Inform. Sci., 10:5 (2016), 1811–1814 | DOI

[18] Noor M. A., Noor K. I., Awan M. U., Safdar F., “On strongly generalized convex functions”, Filomat, 31:18 (2017), 5783–5790 | DOI | MR

[19] Noor M. A., Noor K. I., Safdar F., “Generalized geometrically convex functions and inequalities”, J. Inequal. Appl., 2017 (2017), 202 | DOI | MR | Zbl

[20] Noor M. A., Noor K. I., Safdar F., “Integral inequaities via generalized convex functions”, J. Math. Computer. Sci., 17:4 (2017), 465–476 | MR

[21] Noor M. A., Noor K. I., Iftikhar S., Safdar F., “Integral inequaities for relative harmonic $(s,\eta)$-convex functions”, Appl. Math. Comp. Sci., 1:1 (2015), 27–34 | MR

[22] Noor M. A., Noor K. I., Safdar F., “Integral inequaities via generalized $(\alpha,m)$-convex functions”, J. Nonlinear. Func. Anal., 2017 (2017), 32 | MR | Zbl

[23] Pečarić J. E., Proschan F., Tong Y. L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992 | MR

[24] Sarikaya M. Z., Saglam A., Yildirim H., “On some Hadamard-type inequalities for $h$-convex functions”, J. Math. Inequal., 2:3 (2008), 335–341 | DOI | MR | Zbl

[25] Toader G., “Some generalizations of the convexity”, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, 1985, 329–338 | MR

[26] Tunc M., Kirmaci U., “New inequalities for convex functions”, EÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayi, 3:1 (2010), 91–101

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

[28] Xi B.-Y., Qi F., “Some inequalities of Hermite-Hadamard type for h-convex functions”, Adv. Inequal. Appl., 2:1 (2013), 1–15