Skip to main content

Complex Multivariate Montgomery Identity and Ostrowski and Grüss Inequalities

  • Chapter
  • First Online:
  • 227 Accesses

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

Abstract

We give a general complex multivariate Montgomery type identity which is a representation formula for a complex multivariate function. Using it we produce general tight complex multivariate high order Ostrowski and Grüss type inequalities. The estimates involve \(L_{p}\) norms, any \(1\le p\le \infty \). We include also applications. See also [1].

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
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

Learn about institutional subscriptions

References

  1. G.A. Anastassiou, Complex multivariate montgomery type identity leading to complex multivariate Ostrowski and Grüss inequalities (2019)

    Google Scholar 

  2. S.S. Dragomir, An extension of Ostrowski’s inequality to the complex integral. RGMIA Res. Rep. Call. 21, Art. 112 (2018), 17 pp, http://rgmia.org/papers/v21/v21/v21a112.pdf

  3. S.S. Dragomir, On some Grüss type inequalities for the complex integral. RGMIA Res. Rep. Call. 21, Art. 121 (2018), 12 pp, http://rgmia.org/papers/v21/v21a121.pdf

  4. G. Grüss, Über das Maximum des absoluten Betrages von \(\frac{1}{b-a}\int _{a}^{b}f\left( x\right) g\left( x\right) dx- \frac{1}{\left( b-a\right) ^{2}}\int _{a}^{b}f\left( x\right) dx\int _{a}^{b}g\left( x\right) dx\). Math. Z. 39, 215–226 (1935)

    Google Scholar 

  5. D.S. Mitrinović, J.E. Pečarić, A.M. Fink, Inequalities for Functions and Their Integrals and Derivatives (Kluwer Academic Publishers, Dordrecht, 1994)

    Google Scholar 

  6. A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integral mittelwert. Comment. Math. Helv. 10, 226–227 (1938)

    Article  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). Complex Multivariate Montgomery Identity and Ostrowski and Grüss 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_23

Download citation

Publish with us

Policies and ethics