Morever, some estimates from below and above for the first moments of functions $f:[a,b]\rightarrow \mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\infty )\rightarrow (0,\infty )$ is established.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points.
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Temel Bulgular & Veri:New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points.
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Sonuç & Katkı:Morever, some estimates from below and above for the first moments of functions $f:[a,b]\rightarrow \mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\infty )\rightarrow (0,\infty )$ is established.
New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions $f:[a,b]\rightarrow \mathbb{R}$ about the midpoint $c=(a+b)/2$ are obtained and the reverse Hardy inequality for convex functions $f:(0,\infty )\rightarrow (0,\infty )$ is established.
Sekin, Ç., Tamar, M. E., Aliyev, İ. (2023). New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 4. https://doi.org/10.31801/cfsuasmas.1262668
Amrahov, S. E., A note on Hadamard inequalities for the product of the convex functions, International J. of Research and Reviews in Applied Sciences, 5(2) (2010), 168-170.
Alomari, M., Darus, M. and Dragomir, S. S., New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., 41(4) (2010), 353-359.
Azpetia, A. G., Convex functions and the Hadamard inequality, Revista Colombiana Mat., 28 (1994), 7-12.
Bakula, M. K., Özdemir, M. E. and Pecaric, J., Hadamard-type inequalities for m-convex and $(\alpha,m)$-convex functions. J. Ineq. Pure Appl. Math., 9(4) (2008), Article 96.
Chen, F., Liu, X., On Hermite-Hadamard type inequalities for functions whose second derivatives absolute values are s-convex, ISRN Applied Mathematics, (2014), 1-4, DOI:10.1155/2014/829158.
Dragomir, S. S., Pearce, C. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
Dragomir, S. S., On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math., 3(1) (2002).
El Farissi, A., Simple proof and refinement of Hermite-Hadamard inequality. J. Math. Inequal, 4(3) (2010), 365-369.
Fink, A. M., A best possible Hadamard inequality, Math. Inequal Appl., 1 (1998), 223-230.
Florea, A., Niculescu, C. P., A Hermite-Hadamard inequality for convex-concave symmetric functions, Bull. Soc. Sci. Math. Roum., 50(98) No:2 (2007), 149-156.
Hwang, D. Y., Tseng, K. L. and Yang, G. S., Some Hadamard’s inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11(1) (2007), 63-73, DOI:10.11650/twjm/1500404635.
Ion, D. A., On an inequality due to Amrahov, Annals of University of Craiova, Math. Comp. Sci. Ser., 38(1) (2011), 92-95, DOI 10.52846/ami.v38i1.396.
Kemali, S., Yesilce, I., Adilov, G., B-Convexity, B-1-Convexity and Their Comparison, Numerical Functional Analysis and Optimization, 36(2) (2015), 133-146,. DOI:10.1080/01630563.2014.970641.
Kemali, S., Sezer, S., Tınaztepe, G., Adilov, G., s-Convex functions in the third sense, Korean Journal of Mathematics, 29(3) (2021), 593-602, DOI 10.11568/kjm.2021.29.3.593.
Mercer, A. M. D., A variant of Jensen’s inequality, J. Ineq. Pure and Appl. Math., 4(4) (2003), Article 73.
Mitrinovic, D. S., Pecaric, J. E. and Fink, A. M., Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, 1993.
Niculescu C. P., Persson, L. E., Old and new on the Hermite-Hadamard inequality, Real Anal. Exchange, 29 (2003/2004), 663-686.
Niculescu C. P., Persson, L. E., Convex Functions and Their Applications, A Contemporary Approach, CMS Books in Mathematics, V.23, Springer-Verlag, 2006.
Sarikaya, M. Z., Saglam, A. and Yildirim, H., New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex or quasi-convex, International J. of Open Problems in Comp. Sci. and Math., 5(3) (2012), 1-14.
Sezer, S., Eken, Z., Tınaztepe, G., Adilov, G., p-Convex functions and some of their properties,Numerical Functional Analysis and Optimization, 42(4) (2021), 443-459, DOI:10.1080/01630563.2021.1884876.
Tseng, K. L., Hwang S. R. and Dragomir, S. S., On some new inequalities of Hermite-Hadamard-Fejer type involving convex functions, Demons. Math., 40(1) (2007), 51-64, DOI:10.1515/dema-2007-0108.
Qi, F., Yang, Z. L., Generalizations and refinements of Hermite-Hadamard’s inequality, Rocky Mountain J. Math., 35 (2005), 235-251.