Research article

Integral inequalities of Hermite-Hadamard type for GA-$ F $-convex functions

  • Received: 14 May 2021 Accepted: 22 June 2021 Published: 25 June 2021
  • MSC : 26A51, 26D15, 41A55

  • In the paper, the authors define a notion of geometric-arithmetic-$ F $-convex functions and, via an integral identity and other analytic techniques, establish several integral inequalities of the Hermite-Hadamard type for geometric-arithmetic-$ F $-convex functions.

    Citation: Ye Shuang, Feng Qi. Integral inequalities of Hermite-Hadamard type for GA-$ F $-convex functions[J]. AIMS Mathematics, 2021, 6(9): 9582-9589. doi: 10.3934/math.2021557

    Related Papers:

  • In the paper, the authors define a notion of geometric-arithmetic-$ F $-convex functions and, via an integral identity and other analytic techniques, establish several integral inequalities of the Hermite-Hadamard type for geometric-arithmetic-$ F $-convex functions.



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    [1] M. Adamek, On a problem connected with strongly convex functions, Math. Inequal. Appl., 19 (2016), 1287–1293.
    [2] M. Adamek, On Hermite-Hadamard type inequalities for $F$-convex functions, J. Math. Inequal., 14 (2020), 867–874.
    [3] R. F. Bai, F. Qi, B.Y. Xi, Hermite-Hadamard type inequalities for the $m$- and $(\alpha, m)$-logarithmically convex functions, Filomat, 27 (2013), 1–7. doi: 10.2298/FIL1301001B
    [4] J. Cao, H. M. Srivastava, Z. G. Liu, Some iterated fractional $q$-integrals and their applications, Fract. Calc. Appl. Anal., 21 (2018), 672–695. doi: 10.1515/fca-2018-0036
    [5] 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.
    [6] Y. Hua, Hermite-Hadamard type inequality of GA-convex function, Coll. Math., 24 (2008), 147–149.
    [7] C. E. M. Pearce, J. Pecaric, Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett., 13 (2000), 51–55.
    [8] F. Qi, B. Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasi-convex functions, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 333–342. doi: 10.1007/s12044-014-0182-7
    [9] F. Qi, B. Y. Xi, Some integral inequalities of Simpson type for GA-$\varepsilon$-convex functions, Georgian Math. J., 20 (2013), 775–788.
    [10] F. Qi, T. Y. Zhang, B. Y. Xi, Hermite-Hadamard-type integral inequalities for functions whose first derivatives are convex, Ukr. Math. J., 67 (2015), 625–640. doi: 10.1007/s11253-015-1103-3
    [11] Y. Shuang, H. P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometric-arithmetically $s$-convex functions, Analysis, 33 (2013), 197–208. doi: 10.1524/anly.2013.1192
    [12] B. Y. Xi, R. F. Bai, F. Qi, Hermite-Hadamard type inequalities for the $m$- and $(\alpha, m)$-geometrically convex functions, Aequationes Math., 84 (2012), 261–269. doi: 10.1007/s00010-011-0114-x
    [13] B. Y. Xi, F. Qi, Hermite-Hadamard type inequalities for geometrically $r$-convex functions, Stud. Sci. Math. Hungar., 51 (2014), 530–546.
    [14] B. Y. Xi, F. Qi, Inequalities of Hermite-Hadamard type for extended $s$-convex functions and applications to means, J. Nonlinear Convex Anal., 16 (2015), 873–890.
    [15] B. Y. Xi, F. Qi, Some inequalities of Hermite-Hadamard type for geometrically $P$-convex functions, Adv. Stud. Contemp. Math., 26 (2016), 211–220.
    [16] B. Y. Xi, F. Qi, T. Y. Zhang, Some inequalities of Hermite-Hadamard type for $m$-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357–361. doi: 10.2306/scienceasia1513-1874.2015.41.357
    [17] T. Y. Zhang, A. P. Ji, F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Le Matematiche, 68 (2013), 229–239.
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