Geodesic
Some new generalizations of Hadamard--type Midpoint inequalities involving fractional integrals
Problemy analiza, Tome 9 (2020) no. 3, pp. 66-82

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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 $n^{2}$ times. A dependency between accuracy of the absolute error ($\varepsilon $) of the upper limit of the Hadamard inequality and the number ($n$) of lower intervals is obtained.
Keywords: convexity, Hadamard inequality, Holder's inequality, Power-mean inequality, Riemann-Liouville fractional integrals. 
@article{PA_2020_9_3_a4,
     author = {B. Bayraktar},
     title = {Some new generalizations of {Hadamard--type} {Midpoint} inequalities involving fractional integrals},
     journal = {Problemy analiza},
     pages = {66--82},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2020_9_3_a4/}
}
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B. Bayraktar. Some new generalizations of Hadamard--type Midpoint inequalities involving fractional integrals. Problemy analiza, Tome 9 (2020) no. 3, pp. 66-82. http://geodesic.mathdoc.fr/item/PA_2020_9_3_a4/