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Fractional Simpson Like Type Inequalities for Differentiable s-Convex Functions

S. Bouhadjar (1) and B. Meftah (2)

(1,2) Departement des Mathematiques, Faculte des mathematiques, de l’informatique et des sciences de la matiere, Universite 8 mai 1945 Guelma, Algeria

Email address: (1) s.bouhadjar@yahoo.fr

Email address: (2) badrimeftah@yahoo.fr

Doi : https://doi.org/10.47013/16.3.12

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 563 - 584

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Received on: July 24, 2022;                                         Accepted on: Dec. 14, 2022

 Abstract. Convexity inequalities are very important for fractional calculus and its efficiency in many applied sciences. This field has become increasingly popular and represents a powerful tool for estimating errors of quadrature formulas. In this paper, we seek to develop new four-point Simpson-type inequalities involving Riemenn-Liouville integral operators. To do this, we first propose a new integral identity. By using this identity we establish some new fractional Simpson like type inequalities for functions whose first derivatives are s-convex in the second sense.
Some particular cases are also discussed. We provid at the end some applications to special means to demonstrate the effectiveness of our results.

Keywords: 3/8-Simpson inequality, Riemann-Liouville integral operators, s-convex functions, Holder inequality.