Geodesic
Simpson's Type Inequalities via the Katugampola Fractional Integrals for $s$-Convex Functions
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 5, p. 709 .

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oindent In this paper, we introduce some Simpson's type integral inequalities via the Katugampola fractional integrals for functions whose first derivatives at certain powers are $s$-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann--Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann--Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.
Classification : 26D15 26D10, 26A51, 26A33
Keywords: Simpson's type inequalities, Hölder's inequality, $s$-convexity, Katugampola fractional integrals, Riemann--Liouville fractional integrals, Hadamard fractional integrals 
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     author = {Seth Kermausuor},
     title = {Simpson's {Type} {Inequalities} via the {Katugampola} {Fractional} {Integrals} for $s${-Convex} {Functions}},
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Seth Kermausuor. Simpson's Type Inequalities via the Katugampola Fractional Integrals for $s$-Convex Functions. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 5, p. 709 . http://geodesic.mathdoc.fr/item/KJM_2021_45_5_a3/