Аннотация:
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] into n equal sub-intervals. Using this approach, the absolute error of a Midpoint inequality is shown to decrease approximately n2 times. A dependency between accuracy of the absolute error (ε) of the upper limit of the Hadamard inequality and the number (n) of lower intervals is obtained.
\RBibitem{Bay20}
\by B.~Bayraktar
\paper Some new generalizations of Hadamard--type Midpoint inequalities involving fractional integrals
\jour Пробл. анал. 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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Эта публикация цитируется в следующих 9 статьяx:
J. E. Nápoles, P. M. Guzmán, B. Bayraktar, “Milne-type integral inequalities for modified (h,m)-convex functions on fractal sets”, Пробл. анал. 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
Б. Р. Байрактаров, А. Х. Аттаев, В. Ч. Кудаев, “Некоторые обобщенные неравенства типа Адамара через дробные интегралы”, Изв. вузов. Матем., 2021, № 2, 3–18; 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 k-Riemann–Liouville fractional integrals operators”, Пробл. анал. Issues Anal., 10(28):1 (2021), 3–22
B. Bayraktar, M. Emin Özdemir, “Generalization of Hadamard-type trapezoid inequalities for fractional integral operators”, Уфимск. матем. журн., 13:1 (2021), 119–130; 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)-convex functions”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 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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