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Keywords = dual Simpson inequality

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13 pages, 293 KiB  
Article
On s-Convexity of Dual Simpson Type Integral Inequalities
by Tarek Chiheb, Hamid Boulares, Moheddine Imsatfia, Badreddine Meftah and Abdelkader Moumen
Symmetry 2023, 15(3), 733; https://doi.org/10.3390/sym15030733 - 15 Mar 2023
Cited by 3 | Viewed by 1210
Abstract
Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this study, some symmetric dual Simpson type integral inequalities for the classes of s-convex, bounded and Lipschitzian functions are proposed. The obtained results are based on a new identity [...] Read more.
Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this study, some symmetric dual Simpson type integral inequalities for the classes of s-convex, bounded and Lipschitzian functions are proposed. The obtained results are based on a new identity and the use of some standard techniques such as Hölder as well as power mean inequalities. We give at the end some applications to the estimation of quadrature rules and to particular means. Full article
(This article belongs to the Special Issue Fractional-Order Systems and Its Applications in Engineering)
17 pages, 340 KiB  
Article
Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set
by Abdelghani Lakhdari, Wedad Saleh, Badreddine Meftah and Akhlad Iqbal
Fractal Fract. 2022, 6(12), 710; https://doi.org/10.3390/fractalfract6120710 - 29 Nov 2022
Cited by 18 | Viewed by 1577
Abstract
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result. Using this new identity along with generalized Hölder’s inequality and generalized [...] Read more.
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result. Using this new identity along with generalized Hölder’s inequality and generalized power mean inequality, we establish some new variants of fractal corrected dual-Simpson-type integral inequalities. Furthermore, some applications for error estimates of quadrature formulas as well as some special means involving arithmetic and p-logarithmic mean are offered to demonstrate the efficacy of our findings. Full article
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications)
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