New Inequalities of Simpson’s type for differentiable functions via generalized convex function

Farooq, Shan E.; Shabir, Khurram; Qaisar, Shahid; Ahmad, Farooq; Almatroud, O. A.

doi:10.5802/crmath.152

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New Inequalities of Simpson’s type for differentiable functions via generalized convex function

Farooq, Shan E.¹ ; Shabir, Khurram ² ; Qaisar, Shahid ³ ; Ahmad, Farooq ^4,⁵ ; Almatroud, O. A.⁵

¹ Department of Mathematics, Government College University, Lahore, Punjab, Pakistan
² Department of Mathematics, Government College University, Lahore, Punjab, Pakistan.
³ Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Pakistan.
⁴ Department of Mathematics, College of Sciences, University of Ha’il, Ha’il, KSA.
⁵ School of Mechanical and Aerospace Engineering, NANYANG Technological University, Singapore.

Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 137-147.

Résumé

This article presents some new inequalities of Simpson’s type for differentiable functions by using $(α, m)$ -convexity. Some results for concavity are also obtained. These new estimates improve on the previously known ones. Some applications for special means of real numbers are also provided.

Reçu le : 2020-07-19
Révisé le : 2020-08-16
Accepté le : 2020-11-17
Publié le : 2021-03-17

DOI : 10.5802/crmath.152

Classification : 26A15, 26A51, 26D10

Affiliations des auteurs :

Farooq, Shan E. ¹ ; Shabir, Khurram ² ; Qaisar, Shahid ³ ; Ahmad, Farooq ^{4, 5} ; Almatroud, O. A. ⁵

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     author = {Farooq, Shan E. and Shabir, Khurram and Qaisar, Shahid and Ahmad, Farooq and Almatroud, O. A.},
     title = {New {Inequalities} of {Simpson{\textquoteright}s} type for differentiable functions via generalized convex function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {137--147},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {2},
     year = {2021},
     doi = {10.5802/crmath.152},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.152/}
}

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Farooq, Shan E.; Shabir, Khurram; Qaisar, Shahid; Ahmad, Farooq; Almatroud, O. A. New Inequalities of Simpson’s type for differentiable functions via generalized convex function. Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 137-147. doi : 10.5802/crmath.152. http://www.numdam.org/articles/10.5802/crmath.152/

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