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Complex Multivariate Fink Identity and Complex Multivariate Ostrowski and Grüss Inequalities

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Intelligent Analysis: Fractional Inequalities and Approximations Expanded

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

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Abstract

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

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References

  1. G.A. Anastassiou, Complex multivariate Fink type identity applied to complex multivariate Ostrowski and Grüss inequalities. Indian J. Math. 61(2), 199–237 (2019)

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  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. S.S. Dragomir, An identity of Fink type for the integral of analytic complex function on paths from general domains. RGMIA Res. Rep. Call. 22, Art. 11 (2019), 18 pp, http://rgmia.org/papers/v22/v22a11.pdf

  5. A.M. Fink, Bounds on the deviation of a function from its averages. Czechoslo. Math. J. 42(117)(2), 289–310 (1992)

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

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Correspondence to George A. Anastassiou .

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Anastassiou, G.A. (2020). Complex Multivariate Fink Identity and Complex Multivariate 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_24

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