New type of inequalities involving differentiable \(h\)-convexity with applications

Volume 37, Issue 3, pp 287--296 https://dx.doi.org/10.22436/jmcs.037.03.03

Publication Date: October 04, 2024 Submission Date: August 05, 2024 Revision Date: August 30, 2024 Accteptance Date: September 06, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 149 Downloads
• 275 Views

Authors

O‎. ‎B‎. Almutairi - Department of Mathematics, ‎University of Hafr Al-Batin, ‎Hafr Al-Batin‎, ‎31991, ‎Saudi Arabia.

Abstract

‎In this article‎, ‎we explore the type of integral inequalities using Hölder inequality together with the class of \(h\)-convexity‎. ‎Also‎, ‎we present some trapezoid-type inequalities for the class of mappings whose second derivative in absolute value at certain power is \(h\)-convex‎. ‎The applications to special means of some results obtained are equally discussed‎. ‎In some selected cases‎, ‎several previous results were generalized‎.

Share and Cite

Keywords

• \(h\)-Convex function
• integral inequality
• Hölder inequality
• power-mean inequality

MSC

•  26A33
•  26D10
•  26B25
•  26D15

References

• [1] R. P. Agarwal, M. Bohner, M. Özbekler, Lyapunov inequalities and applications, Springer, Cham (2021)
  • View Article
  • MathSciNet
  • Google Scholar


• [2] M. A. Ali, H. Budak, M. Feˇckan, S. Khan, A new version of q-Hermite-Hadamard’s midpoint and trapezoid type inequalities for convex functions, Math. Slovaca, 73 (2023), 369–386
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] B. Bayraktar, P. Kórus, J. E. Nápoles Valdés, New Jensen-type integral inequalities via modified (h,m)-convexity and their applications, Acta Math. Univ. Comenian. (N.S.), 92 (2023), 213–223
  • View Article
  • Google Scholar


• [4] B. Bayraktar, J. E. Nápoles, F. Rabossi, Some refinements of the Hermite-Hadamard inequality with the help of weighted integrals, Ukrainian Math. J., 75 (2023), 842–860
  • View Article
  • Google Scholar
  • MATH


• [5] B. Bayraktar, J. E. Nápoles Valdés, Integral inequalities for mappings whose derivatives are (h,m, s)-convex modified of second type via Katugampola integrals, An. Univ. Craiova Ser. Mat. Inform., 49 (2022), 371–383
  • View Article
  • Google Scholar
  • MATH


• [6] B. Benaissa, M. Z. Sarikaya, Some Hardy-type integral inequalities involving functions of two independent variables, Positivity, 25 (2021), 853–866
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] D. D. Demir, G. ¸Sanal, Some Perturbed Trapezoid Inequalities for n-times Differentiable Strongly log-Convex Functions, Celal Bayar Univ. J. Sci., 18 (2022), 355–363
  • View Article
  • Google Scholar


• [8] S. S. Dragomir„ R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91–95
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] I. ˙I¸scan, T. Toplu, F. Yetgin, Some new inequalities on generalization of Hermite-Hadamard and Bullen type inequalities, applications to trapezoidal and midpoint formula, Kragujevac J. Math., 45 (2021), 647–657
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] M. A. Latif, A. Kashuri, S. Hussain, M. R. Delavar, Trapezium-type inequalities for h-preinvex functions and their applications, Filomat, 36 (2022), 3393–3404
  • View Article
  • MathSciNet
  • Google Scholar


• [11] D. S. Mitrinovi´c, J. E. Peˇcari´c, A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers Group, Dordrecht (1993)
  • View Article
  • MathSciNet
  • Google Scholar


• [12] H. Kara, S. Erden, H. Budak, Hermite-Hadamard, trapezoid and midpoint type inequalities involving generalized fractional integrals for convex functions, Sahand Commun. Math. Anal., 20 (2023), 85–107
  • View Article
  • Google Scholar
  • MATH


• [13] P. Kórus, J. J. E. Nápoles Valdés, On some integral inequalities for (h,m)-convex functions in a generalized framework, Carpathian Math. Publ., 15 (2023), 137–149
  • View Article
  • Google Scholar


• [14] P. Kórus, J. J. E. Nápoles Valdés, Some Hermite–Hadamard inequalities involving weighted integral operators via (h, s, m)-convex functions, TWMS J. of Apl. Eng. Math., 13 (2023), 1461–1471
  • View Article
  • Google Scholar


• [15] M. Rostamian Delavar, On Fejér’s inequality: generalizations and applications, J. Inequal. Appl., 2023 (2023), 28 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] M. Z. Sarikaya, A. Saglam, H. Yildirim, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (2008), 335–341
  • View Article
  • MathSciNet
  • Google Scholar


• [17] J. E. N. Valdés, F. Rabossi, A. D. Samaniego, Convex functions: Ariadne’s thread or Charlotte’s Spiderweb?, Adv. Math. Models Appl., 25 (2020), 176–191
  • View Article
  • Google Scholar


• [18] S. Varošanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303–311
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] Ç. Yıldız, B. Yergöz, A. Yergöz, On new general inequalities for s-convex functions and their applications, J. Inequal. Appl., 2023 (2023), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] Ç. Yıldız, A. Yergöz, An investigation into inequalities obtained through the new lemma for exponential type convex functions, Filomat, 37 (2023), 5149–5163
  • View Article
  • MathSciNet
  • Google Scholar


• [21] D. Zhao, T. An, G. Ye, W. Liu, New Jensen and Hermite-Hadamard type inequalities for h-convex interval-valued functions, J. Inequal. Appl., 2018 (2018), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] S.-S. Zhou, G. Farid, A. Ahmad, Fractional versions of Minkowski-type integral inequalities via unified Mittag-Leffler function, Adv. Contin. Discrete Models, 2022 (2022), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar