Multivariate Iyengar Inequalities for Radial Functions

  • George A. AnastassiouEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 886)


Here we present a variety of multivariate Iyengar type inequalities for radial functions defined on the shell and ball. Our approach is based on the polar coordinates in \(\mathbb {R}^{N}\), \(N\ge 2\), and the related multivariate polar integration formula. Via this method we transfer well-known univariate Iyengar type inequalities and univariate author’s related results into multivariate Iyengar inequalities. See also [3].


  1. 1.
    R.P. Agarwal, S.S. Dragomir, An application of Hayashi’s inequality for differentiable functions. Comput. Math. Appl. 6, 95–99 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    G.A. Anastassiou, Fractional Differentiation Inequalities. Research Monograph (Springer, New York, 2009)Google Scholar
  3. 3.
    G.A. Anastassiou, Multivariate Iyengar type inequalities for radial functions. Problemy Analiza - Issues of Analysis 8(26), 3–27 (2019), No. 2MathSciNetCrossRefGoogle Scholar
  4. 4.
    G.A. Anastassiou, General Iyengar type inequalities. J. Comput. Anal. Appl. 28(5), 786–797 (2020)Google Scholar
  5. 5.
    Xiao-Liang Cheng, The Iyengar-type inequality. Appl. Math. Lett. 14, 975–978 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    K.S.K. Iyengar, Note on an inequality. Math. Student 6, 75–76 (1938)zbMATHGoogle Scholar
  7. 7.
    Z. Liu, Note on Iyengar’s inequality, Univ. Beograd Publ. Elektrotechn. Fak., Ser. Mat. 16, 29-35 (2005)Google Scholar
  8. 8.
    F. Qi, Further generalizations of inequalities for an integral. Univ. Beograd Publ. Elektrotechn. Fak. Ser. Mat. 8, 79–83 (1997)Google Scholar
  9. 9.
    W. Rudin, Real and Complex Analysis, International Student edn. (Mc Graw Hill, London, 1970)Google Scholar
  10. 10.
    D. Stroock, A Concise Introduction to the Theory of Integration, 3rd edn. (Birkhaüser, Boston, 1999)zbMATHGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

Personalised recommendations