Research article

Estimation-type results with respect to the parameterized (p, q)-integral inequalities

  • Received: 30 September 2019 Accepted: 06 December 2019 Published: 12 December 2019
  • MSC : 05A30, 34A08, 26A33, 26D15

  • We establish a (p, q)-integral identity with parameters and certain new (p, q)-integral inequalities of different types through (p, q)-differentiable mappings. Many results obtained in this article provide significant extensions of other related results given in the literature. Furthermore, we construct three examples to illustrate the investigated results.

    Citation: Chunyan Luo, Tingsong Du, Muhammad Uzair Awan, Yao Zhang. Estimation-type results with respect to the parameterized (p, q)-integral inequalities[J]. AIMS Mathematics, 2020, 5(1): 568-586. doi: 10.3934/math.2020038

    Related Papers:

  • We establish a (p, q)-integral identity with parameters and certain new (p, q)-integral inequalities of different types through (p, q)-differentiable mappings. Many results obtained in this article provide significant extensions of other related results given in the literature. Furthermore, we construct three examples to illustrate the investigated results.


    加载中


    [1] M. Alomari, M. Darus and S. S. Dragomir, New inequalities of Simpson's type for s-convex functions with applications, Research Report Collection, 12 (2009), 1-18.
    [2] N. Alp, M. Z. Sarikaya, M. Kunt, et al. q-Hermite-Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, Journal of King Saud University-Science, 30 (2018), 193-203. doi: 10.1016/j.jksus.2016.09.007
    [3] M. U. Awan, G. Cristescu, M. A. Noor, et al. Upper and lower bounds for Riemann type quantum integrals of preinvex and preinvex dominated functions, U.P.B. Sci. Bull., Series A, 79 (2017), 33-44.
    [4] M. Kunt, İ. İşcan, N. Alp, et al. (p, q)-Hermite-Hadamard inequalities and (p, q)-estimates for midpoint type inequalities via convex and quasi-convex functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math., 112 (2018), 969-992.
    [5] M. Kunt, M. A. Latif and İ. İşcan, Quantum Hermite-Hadamard type inequality and some estimates of quantum midpoint type inequalities for double integrals, Sigma J. Eng. Nat. Sci., 37 (2019), 207-223.
    [6] M. A. Latif, S. S. Dragomir and E. Momoniat, Some q-analogues of Hermite-Hadamard inequality of functions of two variables on finite rectangles in the plane, Journal of King Saud UniversityScience, 29 (2017), 263-273. doi: 10.1016/j.jksus.2016.07.001
    [7] W. J. Liu and H. F. Zhuang, Some quantum estimates of Hermite-Hadamard inequalities for convex functions, J. Appl. Anal. Comput., 7 (2017), 501-522.
    [8] M. A. Noor, K. I. Noor and M. U. Awan, Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput., 251 (2015), 675-679.
    [9] L. Riahi, M. U. Awan and M. A. Noor, Some complementary q-bounds via different classes of convex functions, U.P.B. Sci. Bull., Series A, 79 (2017), 171-182.
    [10] W. Sudsutad, S. K. Ntouyas and J. Tariboon, Integral inequalities via fractional quantum calculus, J. Inequal. Appl., 2016 (2016), 81.
    [11] W. Sudsutad, S. K. Ntouyas and J. Tariboon, Quantum integral inequalities for convex functions, J. Math. Inequal., 9 (2015), 781-793.
    [12] J. Tariboon and S. K. Ntouyas, Quantum integral inequalities on finite intervals, J. Inequal. Appl., 2014 (2014), 121.
    [13] J. Tariboon, S. K. Ntouyas and P. Agarwal, New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations, Adv. Differ. Equ., 2015 (2015), 18.
    [14] M. Tunç and E. Göv, Some integral inequalities via (p, q)-calculus on finite intervals, RGMIA Res. Rep. Coll., 19 (2016), 1-12.
    [15] B. Y. Xi and F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42 (2013), 243-257.
    [16] W. G. Yang, Some new Fejér type inequalities via quantum calculus on finite intervals, ScienceAsia, 43 (2017), 123-134. doi: 10.2306/scienceasia1513-1874.2017.43.123
    [17] Y. Zhang, T. S. Du, H. Wang, et al. Different types of quantum integral inequalities via (α, m)- convexity, J. Inequal. Appl., 2018 (2018), 264.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2737) PDF downloads(387) Cited by(4)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog