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Weighted Simpson-like type inequalities for quasi-convex functions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Strony
313--322
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Laboratoire des Surfaces et Interfaces des Couches Minces (LECIMS), Université Badji Mokhtar-Annaba, Annaba, 23000 Algeria
  • Laboratoire des Surfaces et Interfaces des Couches Minces (LECIMS), Université Badji Mokhtar-Annaba, Annaba, 23000 Algeria
Bibliografia
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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] D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 83-88.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [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.
  • [18] B. Meftah and K. Mekalfa, Some weighted trapezoidal inequalities for differentiable log-convex functions, J. Interdiscip. Math. 23 (2020), 1-13.
  • [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.
  • [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.
  • [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.
  • [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.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ed10930a-576c-4528-b456-a793de390341
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