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Weighted Simpson-like type inequalities for quasi-convex functions

  • Hamida Ayed EMAIL logo and Badreddine Meftah ORCID logo
Published/Copyright: May 3, 2023

Abstract

In this paper, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 2018, Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper.

MSC 2020: 26D15; 26D20; 26A51

References

[1] P. Agarwal, M. Kadakal, İ. İşcan and Y. M. Chu, Better approaches for n-times differentiable convex functions, Mathematics 8 (2020), no. 6, Paper No. 950. 10.3390/math8060950Search in Google Scholar

[2] M. A. Ali, M. Abbas, H. Budak, P. Agarwal, G. Murtaza and Y.-M. Chu, New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions, Adv. Difference Equ. 2021 (2021), Paper No. 64. 10.1186/s13662-021-03226-xSearch in Google Scholar

[3] M. Alomari and M. Darus, On some inequalities of Simpson-type via quasi-convex functions and applications, Transylv. J. Math. Mech. 2 (2010), no. 1, 15–24. Search in Google Scholar

[4] M. Alomari and S. Hussain, Two inequalities of Simpson type for quasi-convex functions and applications, Appl. Math. E-Notes 11 (2011), 110–117. Search in Google Scholar

[5] S. I. Butt, P. Agarwal, S. Yousaf and J. L. G. Guirao, Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications, J. Inequal. Appl. 2022 (2022), Paper No. 1. 10.1186/s13660-021-02735-3Search in Google Scholar

[6] T. Chiheb, N. Boumaza and B. Meftah, Some new Simpson-like type inequalities via preqausiinvexity, Transylv. J. Math. Mech. 12 (2020), no. 1, 1–10. Search in Google Scholar

[7] S. S. Dragomir, R. P. Agarwal and P. Cerone, On Simpson’s inequality and applications, J. Inequal. Appl. 5 (2000), no. 6, 533–579. 10.1155/S102558340000031XSearch in Google Scholar

[8] F. Ertuğral and M. Z. Sarikaya, Simpson type integral inequalities for generalized fractional integral, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 4, 3115–3124. 10.1007/s13398-019-00680-xSearch in Google Scholar

[9] J. Hua, B.-Y. Xi and F. Qi, Some new inequalities of Simpson type for strongly s-convex functions, Afr. Mat. 26 (2015), no. 5–6, 741–752. 10.1007/s13370-014-0242-2Search in Google Scholar

[10] D. A. Ion, Some estimates on the Hermite–Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 83–88. Search in Google Scholar

[11] S. Jain, K. Mehrez, D. Baleanu and P. Agarwal, Certain Hermite–Hadamard inequalities for logarithmically convex functions with applications, Mathematics 7 (2019), no. 2, Paper No. 163. 10.3390/math7020163Search in Google Scholar

[12] A. Kashuri, B. Meftah and P. O. Mohammed, Some weighted Simpson type inequalities for differentiable s-convex functions and their applications, J. Frac. Calc. Nonlinear Sys. 1 (2020), no. 1, 75–94. 10.48185/jfcns.v1i1.150Search in Google Scholar

[13] A. Kashuri, B. Meftah, P. O. Mohammed, A. A. Lupa, B. Abdalla, Y. S. Hamed and T. Abdeljawad, Fractional weighted Ostrowski type inequalities and their applications, Symmetry 13 (2021), no. 6, Paper No. 968. 10.3390/sym13060968Search in Google Scholar

[14] W. Liu, Some Simpson type inequalities for h-convex and ( α , m ) -convex functions, J. Comput. Anal. Appl. 16 (2014), no. 5, 1005–1012. Search in Google Scholar

[15] C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 (2018), Paper No. 332. 10.1186/s13660-018-1924-3Search in Google Scholar PubMed PubMed Central

[16] C. Luo, Y. Yu and T. Du, Estimates of bounds on the weighted Simpson type inequality and their applications, AIMS Math. 5 (2020), no. 5, 4644–4661. 10.3934/math.2020298Search in Google Scholar

[17] B. Meftah and D. Bouchemel, Note on the weighted midpoint type inequalities having the Hölder condition, J. Frac. Calc. Nonlinear Sys. 1 (2021), no. 2, 51–59. Search in Google Scholar

[18] B. Meftah and K. Mekalfa, Some weighted trapezoidal inequalities for differentiable log -convex functions, J. Interdiscip. Math. 23 (2020), 1–13. 10.1080/09720502.2020.1721640Search in Google Scholar

[19] B. Meftah and K. Mekalfa, Some weighted trapezoidal type inequalities via h-preinvexity, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24(542) (2020), 81–97. 10.21857/9xn31coznySearch in Google Scholar

[20] B. Meftah and A. Souahi, Some weighted Ostrowski-type inequalities for differentiable preinvex functions, Math. Methods Appl. Sci. 44 (2021), no. 18, 14892–14914. 10.1002/mma.7751Search in Google Scholar

[21] K. Mehrez and P. Agarwal, New Hermite–Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350 (2019), 274–285. 10.1016/j.cam.2018.10.022Search in Google Scholar

[22] M. Z. Sarikaya, E. Set and M. E. Ozdemir, On new inequalities of Simpson’s type for s-convex functions, Comput. Math. Appl. 60 (2010), no. 8, 2191–2199. 10.1016/j.camwa.2010.07.033Search in Google Scholar

Received: 2022-09-11
Revised: 2023-03-06
Accepted: 2023-03-15
Published Online: 2023-05-03
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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