Skip to main content

Part of the book series: Studies in Computational Intelligence ((SCI,volume 886))

  • 233 Accesses

Abstract

Here we extend advanced known Iyengar type inequalities to Choquet integrals setting with respect to distorted Lebesgue measures and for monotone functions. See also [2].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R.P. Agarwal, S.S. Dragomir, An application of Hayashi’s inequality for differentiable functions. Comput. Math. Appl. 6, 95–99 (1996)

    Article  MathSciNet  Google Scholar 

  2. G. Anastassiou, Choquet-Iyengar type advanced inequalities. J. Comput. Anal. Appl. 28(1), 166–179 (2020)

    Google Scholar 

  3. G. Anastassiou, Choquet integral analytic inequalities. Studia Mathematica Babes-Bolyai, accepted for publication (2018)

    Google Scholar 

  4. X.-L. Cheng, The Iyengar-type inequality. Appl. Math. Lett. 14, 975–978 (2001)

    Article  MathSciNet  Google Scholar 

  5. G. Choquet, Theory of capacities. Ann. Inst. Fourier (Grenoble) 5, 131–295 (1953)

    Article  MathSciNet  Google Scholar 

  6. D. Denneberg, Non-additive Measure and Integral (Kluwer Academic Publishers, Boston, 1994)

    Book  Google Scholar 

  7. I. Franjic, J. Pecaric, I. Peric, Note on an Iyengar type inequality. Appl. Math. Lett. 19, 657–660 (2006)

    Article  MathSciNet  Google Scholar 

  8. K.S.K. Iyengar, Note on an inequality. Math. Stud. 6, 75–76 (1938)

    MATH  Google Scholar 

  9. Z. Liu, Note on Iyengar’s inequality. Univ. Beograde Publ. Elektrotechn. Fak. Ser. Mat. 16, 29–35 (2005)

    Google Scholar 

  10. F. Qi, Further generalizations of inequalities for an integral. Univ. Beograd Publ. Elektrotechn. Fak. Ser. Mat. 8, 79–83 (1997)

    Google Scholar 

  11. M. Sugeno, A note on derivatives of functions with respect to fuzzy measures. Fuzzy Sets Syst. 222, 1–17 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George A. Anastassiou .

Rights and permissions

Reprints and permissions

Copyright information

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

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Anastassiou, G.A. (2020). Choquet–Iyengar Advanced Inequalities. In: Intelligent Analysis: Fractional Inequalities and Approximations Expanded. Studies in Computational Intelligence, vol 886. Springer, Cham. https://doi.org/10.1007/978-3-030-38636-8_10

Download citation

Publish with us

Policies and ethics