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Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities

Year 2019, Volume: 2 Issue: 2, 161 - 175, 27.06.2019
https://doi.org/10.33434/cams.556815

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\leq p\leq \infty $. We include also applications.

References

  • [1] A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integral mittelwert, Comment. Math. Helv. 10 (1938), 226-227.
  • [2] 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(1935), 215-226.
  • [3] D. S. Mitrinovic, J.E. Pecaric, A.M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
  • [4] S. S. Dragomir, An extension of Ostrowski’s inequality to the Complex integral, RGMIA Res. Rep. Call. 21 (2018), Art. 112, 17 pp, [http://rgmia.org/papers/v21/v21/v21a112.pdf].
  • [5] S. S. Dragomir, On some Gr¨uss type inequalities for the complex integral, RGMIA Res. Rep. Call. 21 (2018), Art. 121, 12 pp, [http://rgmia.org/papers/v21/v21a121.pdf].
Year 2019, Volume: 2 Issue: 2, 161 - 175, 27.06.2019
https://doi.org/10.33434/cams.556815

Abstract

References

  • [1] A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integral mittelwert, Comment. Math. Helv. 10 (1938), 226-227.
  • [2] 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(1935), 215-226.
  • [3] D. S. Mitrinovic, J.E. Pecaric, A.M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
  • [4] S. S. Dragomir, An extension of Ostrowski’s inequality to the Complex integral, RGMIA Res. Rep. Call. 21 (2018), Art. 112, 17 pp, [http://rgmia.org/papers/v21/v21/v21a112.pdf].
  • [5] S. S. Dragomir, On some Gr¨uss type inequalities for the complex integral, RGMIA Res. Rep. Call. 21 (2018), Art. 121, 12 pp, [http://rgmia.org/papers/v21/v21a121.pdf].
There are 5 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

George Anastassıou 0000-0002-3781-9824

Publication Date June 27, 2019
Submission Date April 22, 2019
Acceptance Date June 14, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Anastassıou, G. (2019). Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities. Communications in Advanced Mathematical Sciences, 2(2), 161-175. https://doi.org/10.33434/cams.556815
AMA Anastassıou G. Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities. Communications in Advanced Mathematical Sciences. June 2019;2(2):161-175. doi:10.33434/cams.556815
Chicago Anastassıou, George. “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”. Communications in Advanced Mathematical Sciences 2, no. 2 (June 2019): 161-75. https://doi.org/10.33434/cams.556815.
EndNote Anastassıou G (June 1, 2019) Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities. Communications in Advanced Mathematical Sciences 2 2 161–175.
IEEE G. Anastassıou, “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”, Communications in Advanced Mathematical Sciences, vol. 2, no. 2, pp. 161–175, 2019, doi: 10.33434/cams.556815.
ISNAD Anastassıou, George. “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”. Communications in Advanced Mathematical Sciences 2/2 (June 2019), 161-175. https://doi.org/10.33434/cams.556815.
JAMA Anastassıou G. Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities. Communications in Advanced Mathematical Sciences. 2019;2:161–175.
MLA Anastassıou, George. “Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities”. Communications in Advanced Mathematical Sciences, vol. 2, no. 2, 2019, pp. 161-75, doi:10.33434/cams.556815.
Vancouver Anastassıou G. Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities. Communications in Advanced Mathematical Sciences. 2019;2(2):161-75.

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