A HARMONIC MEAN INEQUALITY FOR
THE EXPONENTIAL INTEGRAL FUNCTION

Abstract

By using purely analytical techniques, we establish a harmonic mean inequality for the classical exponential integral function.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 4
Year: 2021

DOI: 10.12732/ijam.v34i4.4

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References

  1. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphic and Mathematical Tables, Dover Publications, Inc., New York (1965).
  2. [2] H. Alzer and G. Jameson, A harmonic mean inequality for the digamma function and related results, Rend. Sem. Mat. Univ. Padova, 137 (2017), 203-209.
  3. [3] P.K. Bhandari and S.K. Bissu, On some inequalities involving Turan-type inequalities, Cogent Math., 3, No 1 (2016), Article # 1130678.
  4. [4] M. Bouali, A harmonic mean inequality for the q-gamma and q-digamma functions, arXiv:2005.08945 [math.CA] (2020).
  5. [5] C. Chiccoli, S. Lorenzutta and G. Maino, Recent results for generalized exponential integrals, Computers Math. Appl., 19, No 5 (1990), 21-29.
  6. [6] W. Gautschi, A harmonic mean inequality for the gamma function, SIAM J. Math. Anal., 5 (1974), 278-281.
  7. [7] G.J.O. Jameson, The real exponential integrals; Available online at: https://www.maths.lancs.ac.uk/ jameson/expint.pdf.
  8. [8] E. Masina, Useful review on the Exponential-Integral special function, arXiv:1907.12373v1 [math.GM] (2019).
  9. [9] L. Matejicka, Proof of a conjecture on Nielsen’s -function, Probl. Anal. Issues Anal., 8, No 26 (2019), 105-111.
  10. [10] K. Nantomah, Certain Properties of the Nielsen’s -function, Bull. Int. Math. Virtual Inst., 9 (2019), 263-269.
  11. [11] K. Nantomah, Harmonic mean inequalities for hyperbolic functions, Earthline J. Math. Sci., 6, No 1 (2021), 117-129.
  12. [12] K. Nantomah, F. Merovci and S. Nasiru, A generalization of the exponential integral and some associated inequalities, Honam Mathematical J., 39, No 1 (2017), 49-59.
  13. [13] F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark (Eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, London, 2010.
  14. [14] A. Salem, A q-analogue of the exponential integral, Afr. Mat., 24 (2013), 117-125.
  15. [15] B. Sroysang, On the n-th derivative of the exponential integral functions, Communications in Mathematics and Applications, 4, No 2 (2013), 141144.
  16. [16] W.T. Sulaiman, Turan inequalities for the exponential integral functions, Commun. Optim. Theory, 1, No 1 (2012), 35-41.
  17. [17] A. Yakubu, K. Nantomah and M. M. Iddrisu, A p-analogue of the exponential integral function and some properties, Adv. Inequal. Appl., 2020 (2020), Article # 7.
  18. [18] E. Yildirim, Monotonicity properties on k-digamma function and its related inequalities, J. Math. Inequal., 14, No 1 (2020), 161-173.
  19. [19] L. Yin, L-G. Huang, X-L. Lin and Y-L.Wang, Monotonicity, concavity, and inequalities related to the generalized digamma function, Adv. Difference Equ., 2018 (2018), Article # 246.