Abstract:
In this study, we formulate the identity and obtain some generalized inequalities of the Hermite–Hadamard type by using fractional Riemann–Liouville integrals for functions whose absolute values of the second derivatives are convex. The results are obtained by uniformly dividing a segment [a,b][a,b] into nn equal sub-intervals. Using this approach, the absolute error of a Midpoint inequality is shown to decrease approximately n2n2 times. A dependency between accuracy of the absolute error (εε) of the upper limit of the Hadamard inequality and the number (nn) of lower intervals is obtained.
\Bibitem{Bay20}
\by B.~Bayraktar
\paper Some new generalizations of Hadamard--type Midpoint inequalities involving fractional integrals
\jour Probl. Anal. Issues Anal.
\yr 2020
\vol 9(27)
\issue 3
\pages 66--82
\mathnet{http://mi.mathnet.ru/pa307}
\crossref{https://doi.org/10.15393/j3.art.2020.8270}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000590954400004}
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This publication is cited in the following 9 articles:
J. E. Nápoles, P. M. Guzmán, B. Bayraktar, “Milne-type integral inequalities for modified (h,m)(h,m)-convex functions on fractal sets”, Probl. anal. Issues Anal., 13(31):2 (2024), 106–127
Péter Kórus, Juan Eduardo Nápoles Valdés, Bahtiyar Bayraktar, “Weighted Hermite–Hadamard integral inequalities for general convex functions”, MBE, 20:11 (2023), 19929
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh, “New Variant of Hermite–Hadamard, Fejér and Pachpatte-Type Inequality and Its Refinements Pertaining to Fractional Integral Operator”, Fractal Fract, 7:5 (2023), 405
Bahtiyar Bayraktar, Juan Eduardo Napoles-Valdes, “Integral inequalities for mappings whose derivatives are (h,m,s)-convex modied of second type via Katugampola integrals”, AUCMCS, 49:2 (2022), 371
B. Bayraktar, A. H. Attaev, V. Ch. Kudaev, “Some generalized Hadamard–type inequalities via fractional integrals”, Russian Math. (Iz. VUZ), 65:2 (2021), 1–14
S. I. Butt, B. Bayraktar, M. Umar, “Several new integral inequalities via kk-Riemann–Liouville fractional integrals operators”, Probl. anal. Issues Anal., 10(28):1 (2021), 3–22
Ufa Math. J., 13:1 (2021), 119–130
B. Bayraktar, S. I. Butt, Sh. Shaokat, J. E. Nápoles Valdés, “New Hadamard-type inequalities via (s,m1,m2)(s,m1,m2)-convex functions”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:4 (2021), 597–612
“New integral inequalities of Hermite–Hadamard type in a generalized context”, Punjab Univ. j. math., 2021, 765
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