Geodesic
Refinements and reverses of F\'{e}jer's inequalities for convex functions on linear spaces
Problemy analiza, Tome 9 (2020) no. 3, pp. 99-118.

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In this paper, we establish some refinements and reverses of the celebrated Féjer's inequalities for the general case of functions defined on linear spaces. The obtained bounds are in terms of the Gâteaux lateral derivatives. Some applications for norms and semi-inner products in normed linear spaces are also provided.
Keywords: convex functions, integral inequalities, Hermite-Hadamard inequality, Féjer's inequalities. 
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S. S. Dragomir. Refinements and reverses of F\'{e}jer's inequalities for convex functions on linear spaces. Problemy analiza, Tome 9 (2020) no. 3, pp. 99-118. http://geodesic.mathdoc.fr/item/PA_2020_9_3_a6/

[1] Alomari M., Darus M., “Refinements of s-Orlicz convex functions in normed linear spaces”, Int. J. Contemp. Math. Sci., 3:29–32 (2008), 1569–1594 | MR | Zbl

[2] Ciorănescu I., Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Academic Publishers, Dordrecht, 1990 | MR | Zbl

[3] Chen X., “New convex functions in linear spaces and Jensen's discrete inequality”, J. Inequal. Appl., 2013 (2013), 472, 8 pp. | DOI | MR

[4] 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 https://www.emis.de/journals/JIPAM/article183.html?sid=183 | MR | Zbl

[5] 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 https://www.emis.de/journals/JIPAM/article187.html?sid=187 | MR

[6] Dragomir S. S., Pearce C. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000 https://rgmia.org/monographs/hermite_hadamard.html

[7] Dragomir S. S., Semi-inner Products and Applications, Nova Science Publishers, Inc., Hauppauge, NY, 2004, x+222 pp. | MR | Zbl

[8] Khan M. A., Khalid S., Pečarić J., “Improvement of Jensen's inequality in terms of Gâteaux derivatives for convex functions in linear spaces with applications”, Kyungpook Math. J., 52:4 (2012), 495–511 | DOI | MR | Zbl

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

[10] Kikianty E., Dragomir S. S., Cerone P., “Ostrowski type inequality for absolutely continuous functions on segments in linear spaces”, Bull. Korean Math. Soc., 45:4 (2008), 763–780 | DOI | MR | Zbl

[11] Kikianty E., Dragomir S. S., Cerone P., “Sharp inequalities of Ostrowski type for convex functions defined on linear spaces and application”, Comput. Math. Appl., 56:9 (2008), 2235–2246 | DOI | MR | Zbl