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Fractal Fract
Volume 6
Issue 12
10.3390/fractalfract6120710
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Article

Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set

by
Abdelghani Lakhdari
1,
Wedad Saleh
2,*,
Badreddine Meftah
3 and
Akhlad Iqbal
4
1
Department CPST, Higher School of Industrial Technologies, P.O. Box 218, Annaba 23000, Algeria
2
Department of Mathematics, Taibah University, Al-Medina 42353, Saudi Arabia
3
Department of Mathematics, 8 May 1945 University, Guelma 24000, Algeria
4
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
*
Author to whom correspondence should be addressed.
Fractal Fract. 2022, 6(12), 710; https://doi.org/10.3390/fractalfract6120710
Submission received: 6 November 2022 / Revised: 21 November 2022 / Accepted: 24 November 2022 / Published: 29 November 2022
(This article belongs to the Special Issue Fractional Integral Inequalities and Applications)
Versions Notes

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 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.
Keywords: corrected dual-Simpson inequality; local fractional derivatives; local fractional integrals; generalized convex functions; fractal set corrected dual-Simpson inequality; local fractional derivatives; local fractional integrals; generalized convex functions; fractal set

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MDPI and ACS Style

Lakhdari, A.; Saleh, W.; Meftah, B.; Iqbal, A. Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set. Fractal Fract. 2022, 6, 710. https://doi.org/10.3390/fractalfract6120710

AMA Style

Lakhdari A, Saleh W, Meftah B, Iqbal A. Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set. Fractal and Fractional. 2022; 6(12):710. https://doi.org/10.3390/fractalfract6120710

Chicago/Turabian Style

Lakhdari, Abdelghani, Wedad Saleh, Badreddine Meftah, and Akhlad Iqbal. 2022. "Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set" Fractal and Fractional 6, no. 12: 710. https://doi.org/10.3390/fractalfract6120710

APA Style

Lakhdari, A., Saleh, W., Meftah, B., & Iqbal, A. (2022). Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set. Fractal and Fractional, 6(12), 710. https://doi.org/10.3390/fractalfract6120710

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