Korean J. Math. Vol. 32 No. 3 (2024) pp.365-379
DOI: https://doi.org/10.11568/kjm.2024.32.3.365

A note on Simpson $3/8$ rule for function whose modulus of first derivatives are $s$-convex function with application

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Published: Sep 30, 2024
Keywords:
Simpson 3/8 type inequality, fractional integral, convex function, Hölder inequality, Power-mean inequality
Mathematics Subject Classification:
26D07, 26D10, 26D15

Main Article Content

Arslan Munir
Department of Mathematics, COMSATS University, Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan.
Hüseyin Budak
Department of Mathematics, Duzce University, Duzce, Turkiye.
Hasan Kara
Department of Mathematics, Duzce University, Duzce, Turkiye.
https://orcid.org/0000-0002-2075-944X
Laxmi Rathour
Department of Mathematics,National Institute of Technology, Chaltlang, Aizawl 796 012, Mizoram, India.
Irza Faiz
Department of Mathematics, Government College University Faisalabed, Sahiwal Campus, Pakistan.

Abstract

Researchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the $s$-convex functions. Furthermore, we also include the applications to special means.


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