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New Inequalities of Simpson’s type for differentiable functions via generalized convex function
Shan E. Farooq1  ; Khurram Shabir2 ; Shahid Qaisar3 ; Farooq Ahmad4, 5  ; O. A. Almatroud5
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, Volume 359 (2021) no. 2, pp. 137-147.

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.

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DOI : 10.5802/crmath.152
Classification : 26A15, 26A51, 26D10
Shan E. Farooq 1 ; Khurram Shabir 2 ; Shahid Qaisar 3 ; Farooq Ahmad 4, 5 ; O. A. Almatroud 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.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Shan E. Farooq and Khurram Shabir and Shahid Qaisar and Farooq Ahmad and O. A. Almatroud},
     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},
}
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Shan E. Farooq; Khurram Shabir; Shahid Qaisar; Farooq Ahmad; O. A. Almatroud. New Inequalities of Simpson’s type for differentiable functions via generalized convex function. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 137-147. doi : 10.5802/crmath.152. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.152/

[1] Mohammad Alomari; Maslina Darus; Sever S. Dragomir New inequalities of Simpson’s type for s-convex functions with applications (2009) (published in RGMIA Research report collection, https://rgmia.org/papers/v12n4/Simpson.pdf)

[2] Sever S. Dragomir; Ravi P. Agarwal; Pietro Cerone On Simpson’s inequality and applications, J. Inequal. Appl., Volume 5 (2000) no. 6, pp. 533-579 | MR | Zbl

[3] Sever S. Dragomir; Simon Fitzpatrick The Hadamard inequalities for s-convex functions in the second sense, Demonstr. Math., Volume 32 (1999) no. 4, pp. 687-696 | MR | Zbl

[4] Tingsong Du; Hao Wang; Muhammad Adil Khan; Yao Zhang Certain integral inequalities considering generalized m-convexity on fractal sets and their applications, Fractals-Complex Geometry, Patterns,and Scaling, Fractals, Volume 27 (2019) no. 7, 1950117, 17 pages | Zbl

[5] Uǧur S. Kirmaci Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput., Volume 147 (2004) no. 1, pp. 137-146 | MR | Zbl

[6] Zheng Liu An inequality of Simpson’s type, Proc. A, R. Soc. Lond., Volume 461 (2005) no. 2059, pp. 2155-2158 | MR | Zbl

[7] Vasile G. Mihesan A generalization of the convexity, 1993 (Seminar on functional equations, approximation and convexity, Cluj-Napoca)

[8] Shahid Qaisar; Chuanjiang He; Sabir Hussain A generalizations of Simpson’s type inequality for differentiable functions using α,m -convex functions and applications, J. Inequal. Appl., Volume 2013 (2013), 158, 13 pages | MR | Zbl

[9] Mehmet Zeki Sarikaya; Erhan Set; Muhamet Emin Özdemir On new inequalities of Simpson’s type for convex functions RGMIA Res. (2010) (published in RGMIA Research report collection, https://rgmia.org/papers/v13n1/sso3.pdf) | Zbl

[10] Mehmet Zeki Sarikaya; Erhan Set; Muhamet Emin Özdemir On new inequalities of Simpson’s type for s-convex functions,Computers and Mathematics with Applications, Comput. Math. Appl., Volume 60 (2010) no. 8, pp. 2191-2199 | DOI | Zbl

[11] Erhan Set; Ahmet Ocak Akdemir; Muhamet Emin Özdemir Simpson’s type integral inequalities for convex functions via Riemann–Liouville integrals, Filomat, Volume 31 (2017) no. 14, pp. 4415-4420 | MR

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