Complex Multivariate Montgomery Type Identity Leading to Complex Multivariate Ostrowski and Grüss Inequalities
Öz
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.
Anahtar Kelimeler
Multivariate complex integral Multivariate complex continuous functions Multivariate complex analytic functions Multivariate complex montgomery identity Multivariate complex Ostrowski and Gr\"{u}ss inequalities
Kaynakça
- [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].
Öz
Kaynakça
- [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].
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 27 Haziran 2019 |
| Gönderilme Tarihi | 22 Nisan 2019 |
| Kabul Tarihi | 14 Haziran 2019 |
| Yayımlandığı Sayı | Yıl 2019 |
Kaynak Göster
Cited By
Novel Results based on Generalisation of Some Integral Inequalities for Trigonometrically -P Function
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.16984/saufenbilder.711507
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