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Complex Multivariate Montgomery Identity and Ostrowski and Grüss Inequalities

  • George A. AnastassiouEmail author
Chapter
Part of the Studies in Computational Intelligence book series (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].

References

  1. 1.
    G.A. Anastassiou, Complex multivariate montgomery type identity leading to complex multivariate Ostrowski and Grüss inequalities (2019)Google Scholar
  2. 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. 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. 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. 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. 6.
    A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integral mittelwert. Comment. Math. Helv. 10, 226–227 (1938)CrossRefGoogle 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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