Research article

On some refinements for inequalities involving zero-balanced hypergeometric function

  • Received: 08 June 2020 Accepted: 13 August 2020 Published: 19 August 2020
  • MSC : 33E05, 33C05

  • In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.

    Citation: Tie-Hong Zhao, Zai-Yin He, Yu-Ming Chu. On some refinements for inequalities involving zero-balanced hypergeometric function[J]. AIMS Mathematics, 2020, 5(6): 6479-6495. doi: 10.3934/math.2020418

    Related Papers:

  • In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.


    加载中


    [1] G. J. Hai, T. H. Zhao, Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function, J. Inequal. Appl., 2020 (2020), 1-17. doi: 10.1186/s13660-019-2265-6
    [2] T. H. Zhao, L. Shi, Y. M. Chu, Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means, RACSAM, 114 (2020), 1-14. doi: 10.1007/s13398-019-00732-2
    [3] M. K. Wang, Z. Y. He, Y. M. Chu, Sharp power mean inequalities for the generalized elliptic integral of the first kind, Comput. Meth. Funct. Th., 20 (2020), 111-124. doi: 10.1007/s40315-020-00298-w
    [4] T. H. Zhao, Y. M. Chu, H. Wang, Logarithmically complete monotonicity properties relating to the gamma function, Abstr. Appl. Anal., 2011 (2011), 1-13.
    [5] J. M. Shen, Z. H. Yang, W. M. Qian, et al. Sharp rational bounds for the gamma function, Math. Inequal. Appl., 23 (2020), 843-853.
    [6] M. K. Wang, H. H. Chu, Y. M. Li, et al. Answers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kind, Appl. Anal. Discrete Math., 14 (2020), 255- 271.
    [7] M. K. Wang, Y. M. Chu, Y. M. Li, et al. Asymptotic expansion and bounds for complete elliptic integrals, Math. Inequal. Appl., 23 (2020), 821-841.
    [8] T. H. Zhao, M. K. Wang, Y. M. Chu, A sharp double inequality involving generalized complete elliptic integral of the first kind, AIMS Math., 5 (2020), 4512-4528. doi: 10.3934/math.2020290
    [9] S. Takeuchi, A new form of the generalized complete elliptic integrals, Kodai Math. J., 39 (2016), 202-226. doi: 10.2996/kmj/1458651700
    [10] I. A. Baloch, Y. M. Chu, Petrović-type inequalities for harmonic h-convex functions, J. Funct. Space., 2020 (2020), 1-7.
    [11] M. U. Awan, N. Akhtar, S. Iftikhar, et al. New Hermite-Hadamard type inequalities for npolynomial harmonically convex functions, J. Inequal. Appl., 2020 (2020), 1-12. doi: 10.1186/s13660-019-2265-6
    [12] M. Adil Khan, J. Pečarić, Y. M. Chu, Refinements of Jensen's and McShane's inequalities with applications, AIMS Math., 5 (2020), 4931-4945. doi: 10.3934/math.2020315
    [13] S. Rashid, R. Ashraf, M. A. Noor, et al. New weighted generalizations for differentiable exponentially convex mapping with application, AIMS Math., 5 (2020), 3525-3546. doi: 10.3934/math.2020229
    [14] M. A. Khan, M. Hanif, Z. A. Khan, et al. Association of Jensen's inequality for s-convex function with Csiszár divergence, J. Inequal. Appl., 2019 (2019), 1-14. doi: 10.1186/s13660-019-1955-4
    [15] S. Rashid, İ. İşcan, D. Baleanu, et al. Generation of new fractional inequalities via n polynomials s-type convexixity with applications, Adv. Differ. Equ., 2020 (2020), 1-20. doi: 10.1186/s13662-019-2438-0
    [16] S. Z. Ullah, M. A. Khan, Y. M. Chu, A note on generalized convex functions, J. Inequal. Appl., 2019 (2019), 1-10. doi: 10.1186/s13660-019-1955-4
    [17] Y. Khurshid, M. A. Khan, Y. M. Chu, Conformable fractional integral inequalities for GG- and GA-convex function, AIMS Math., 5 (2020), 5012-5030. doi: 10.3934/math.2020322
    [18] M. A. Latif, S. Rashid, S. S. Dragomir, et al. Hermite-Hadamard type inequalities for co-ordinated convex and qausi-convex functions and their applications, J. Inequal. Appl., 2019 (2019), 1-33. doi: 10.1186/s13660-019-1955-4
    [19] W. M. Qian, W. Zhang, Y. M. Chu, Bounding the convex combination of arithmetic and integral means in terms of one-parameter harmonic and geometric means, Miskolc Math. Notes, 20 (2019), 1157-1166. doi: 10.18514/MMN.2019.2334
    [20] T. Abdeljawad, S. Rashid, H. Khan, et al. On new fractional integral inequalities for p-convexity within interval-valued functions, Adv. Differ. Equ., 2020 (2020), 1-17. doi: 10.1186/s13662-019-2438-0
    [21] S. S. Zhou, S. Rashid, F. Jarad, et al. New estimates considering the generalized proportional Hadamard fractional integral operators, Adv. Differ. Equ., 2020 (2020), 1-15. doi: 10.1186/s13662-019-2438-0
    [22] S. Hussain, J. Khalid, Y. M. Chu, Some generalized fractional integral Simpson's type inequalities with applications, AIMS Math., 5 (2020), 5859-5883. doi: 10.3934/math.2020375
    [23] L. Xu, Y. M. Chu, S. Rashid, et al. On new unified bounds for a family of functions with fractional q-calculus theory, J. Funct. Space., 2020 (2020), 1-9.
    [24] S. Rashid, A. Khalid, G. Rahman, et al. On new modifications governed by quantum Hahn's integral operator pertaining to fractional calculus, J. Funct. Space., 2020 (2020), 1-12.
    [25] J. M. Shen, S. Rashid, M. A. Noor, et al. Certain novel estimates within fractional calculus theory on time scales, AIMS Math., 5 (2020), 6073-6086. doi: 10.3934/math.2020390
    [26] H. X. Qi, M. Yussouf, S. Mehmood, et al. Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity, AIMS Math., 5 (2020), 6030-6042. doi: 10.3934/math.2020386
    [27] H. Kalsoom, M. Idrees, D. Baleanu, et al. New estimates of q1q2-Ostrowski-type inequalities within a class of n-polynomial prevexity of function, J. Funct. Space., 2020 (2020), 1-13.
    [28] H. Ge-JiLe, S. Rashid, M. A. Noor, et al. Some unified bounds for exponentially tgs-convex functions governed by conformable fractional operators, AIMS Math., 5 (2020), 6108-6123. doi: 10.3934/math.2020392
    [29] A. Iqbal, M. A. Khan, N. Mohammad, et al. Revisiting the Hermite-Hadamard integral inequality via a Green function, AIMS Math., 5 (2020), 6087-6107. doi: 10.3934/math.2020391
    [30] M. B. Sun, Y. M. Chu, Inequalities for the generalized weighted mean values of g-convex functions with applications, RACSAM, 114 (2020), 1-12. doi: 10.1007/s13398-019-00732-2
    [31] T. Abdeljawad, S. Rashid, Z. Hammouch, et al. Some new local fractional inequalities associated with generalized (s, m)-convex functions and applications, Adv. Differ. Equ., 2020 (2020), 1-27.
    [32] X. Z. Yang, G. Farid, W. Nazeer, et al. Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex function, AIMS Math., 5 (2020), 6325-6340. doi: 10.3934/math.2020407
    [33] S. Rashid, F. Jarad, Y. M. Chu, A note on reverse Minkowski inequality via generalized proportional fractional integral operator with respect to another function, Math. Probl. Eng., 2020 (2020), 1-12.
    [34] S. Rashid, M. A. Noor, K. I. Noor, et al. Ostrowski type inequalities in the sense of generalized $\mathcal{K}$-fractional integral operator for exponentially convex functions, AIMS Math., 5 (2020), 2629- 2645.
    [35] Y. Khurshid, M. Adil Khan, Y. M. Chu, Conformable integral version of Hermite-Hadamard-Fejér inequalities via η-convex functions, AIMS Math., 5 (2020), 5106-5120. doi: 10.3934/math.2020328
    [36] S. Rashid, F. Jarad, H. Kalsoom, et al. On Pólya-Szegö and ĆebyĆev type inequalities via general-ized k-fractional integrals, Adv. Differ. Equ., 2020 (2020), 1-18. doi: 10.1186/s13662-019-2438-0
    [37] S. Y. Guo, Y. M. Chu, G. Farid, et al. Fractional Hadamard and Fej´er-Hadamard inequaities associated with exponentially (s, m)-convex functions, J. Funct. Space., 2020 (2020), 1-10.
    [38] I. Abbas Baloch, A. A. Mughal, Y. M. Chu, et al. A variant of Jensen-type inequality and related results for harmonic convex functions, AIMS Math., 5 (2020), 6404-6418. doi: 10.3934/math.2020412
    [39] M. U. Awan, S. Talib, A. Kashuri, et al. Estimates of quantum bounds pertaining to new q-integral identity with applications, Adv. Differ. Equ., 2020 (2020), 1-15. doi: 10.1186/s13662-019-2438-0
    [40] M. U. Awan, S. Talib, M. A. Noor, et al. Some trapezium-like inequalities involving functions having strongly n-polynomial preinvexity property of higher order, J. Funct. Space., 2020 (2020), 1-9.
    [41] G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Functional inequalities for complete elliptic integrals and ratios, SIAM J. Math. Anal., 21 (1990), 536-549. doi: 10.1137/0521029
    [42] H. Alzer, K. Richards, Inequalities for the ratio of complete elliptic integrals, Proc. Amer. Math. Soc., 145 (2017), 1661-1670.
    [43] L. Yin, L. G. Huang, Y. L. Wang, et al. An inequality for generalized complete elliptic integral, J. Inequal. Appl., 2017 (2017), 1-6. doi: 10.1186/s13660-016-1272-0
    [44] K. C. Richards, A note on inequalities for the ratio of zero-balanced hypergeometric functions, Proc. Amer. Math. Soc., 6B (2019), 15-20.
    [45] Z. H. Yang, Y. M. Chu, X. J. Tao, A double inequality for the trigamma function and its applications, Abstr. Appl. Anal., 2014 (2014), 1-9.
  • 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(4832) PDF downloads(291) Cited by(195)

Article outline

Figures and Tables

Figures(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog