General Multivariate Iyengar Inequalities

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


Here we give a variety of general multivariate Iyengar type inequalities for not necessarily radial functions defined on the shell and ball.


  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, General Iyengar type inequalities. J. Comput. Anal. Appl. 28(5), 786–797 (2020)Google Scholar
  4. 4.
    G.A. Anastassiou, General Multivariate Iyengar Type Inequalities, Constructive Mathematical Analysis (2019)Google Scholar
  5. 5.
    X.-L. 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. Serija Matematika, vol. 16 (Publikacije Elektrotehnickog fakulteta, 2005), pp. 29–35Google Scholar
  8. 8.
    F. Qi, Further Generalizations of Inequalities for an Integral, Serija Matematika, vol. 8 (Publikacije Elektrotehnickog fakulteta, 1997), pp. 79–83Google 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)Google 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

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