Geodesic
On generalizations of integral inequalities
Problemy analiza, Tome 11 (2022) no. 2, pp. 3-23

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In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequalities.
Keywords: convex function, Hermite–Hadamard inequality, Simpson-type inequality, Lipschitz conditions, Lagrange theorem, Riemann–Liouville fractional integral. 
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     title = {On generalizations of integral inequalities},
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B. Bayraktar; J. E. Nápoles; F. Rabossi. On generalizations of integral inequalities. Problemy analiza, Tome 11 (2022) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/PA_2022_11_2_a0/