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Fractional Maclaurin Type Inequalities for Functions whose First Derivatives are s-Convex Functions

S. Djenaoui (1) and B. Meftah (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) djenaoui.saliha@univ-guelma.dz

Email address: (2) badrimeftah@yahoo.fr

Doi : https://doi.org/10.47013/16.3.7

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 483 - 506

PDF

Received on: July 3, 2022;                                         Accepted on: Oct. 30, 2022

 Abstract. Classical and fractional integral inequalities have become a popular method and a powerful tool for estimating errors of quadrature formulas. Several studies on various types of inequality have been conducted and the literature in this area is vast and diverse. The current study intends to investigate one of the open three-point Newton-Cotes formulae, known as Maclaurin’s formula, using Riemann-Liouville fractional operators. To accomplish so, we first created a new identity.
From this identity and through the s-convexity, we have established some new Maclaurin-type inequalities, we also discussed the cases that can be derived of our finding. Furthermore, various applications for error estimates are offered to demonstrate the efficacy of our primary results.

Keywords: Maclaurin’s formulae, Newton-Cotes quadrature, s-convex functions,...