An extension of trapezoid inequality to the complex integral

Sever Dragomır

doi:10.31801/cfsuasmas.798863

Araştırma Makalesi

Yıl 2021, Cilt: 70 Sayı: 2, 1113 - 1130, 31.12.2021

Sever Dragomır

https://doi.org/10.31801/cfsuasmas.798863

Öz

Kaynakça

Cerone, P., Dragomir, S. S., Trapezoidal-Type Rules From an Inequalities Point of View, Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou (Ed.), CRC Press, NY, 2000, 65-134.
Cerone, P., Dragomir, S. S., Pearce, C. E. M., A generalised trapezoid inequality for functions of bounded variation, Turkish J. Math., 24(2) (2000), 147-163.
Dragomir, S. S., An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Ineq. Pure & Appl. Math., 3(2) (2002), Art. 31. https://www.emis.de/journals/JIPAM/article183.html?sid=183
Dragomir, S. S., An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Ineq. Pure & Appl. Math., 3(3) (2002), Art. 35. https://www.emis.de/journals/JIPAM/article187.html?sid=187
Dragomir, S. S., The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), 495–508.
Dragomir, S. S., Rassias, Th. M. (Eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht, 2002.
Kechriniotis, A. I., Assimakis, N. D., Generalizations of the trapezoid inequalities based on a new mean value theorem for the remainder in Taylor’s formula, J. Inequal. Pure Appl. Math., 7(3) (2006), Article 90, 13 pp.
Liu, Z., Some inequalities of perturbed trapezoid type, J. Inequal. Pure Appl. Math., 7(2) (2006), Article 47, 9 pp.
Mercer, McD. A., On perturbed trapezoid inequalities, J. Inequal. Pure Appl. Math., 7(4) (2006), Article 118, 7 pp. (electronic).
Ostrowski, A., Uber die absolutabweichung einer differentiierbaren funktion von ihrem integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
Ujevic, N., Error inequalities for a generalized trapezoid rule, Appl. Math. Lett. 19(1) (2006), 32–37.

An extension of trapezoid inequality to the complex integral

Yıl 2021, Cilt: 70 Sayı: 2, 1113 - 1130, 31.12.2021

Sever Dragomır

https://doi.org/10.31801/cfsuasmas.798863

Öz

In this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity $| (v - u) f (u) + (w - v) f (w) - \int_{γ} f (z) d z |$ under the assumptions that $γ$ is a smooth path parametrized by $z (t), t \in [a, b], u = z (a), v = z (x)$ with $x \in (a, b)$ and $w = z (b)$ while $f$ is holomorphic in $G$ , an open domain and $γ \in G$ . An application for circular paths is also given.

Anahtar Kelimeler

Complex integral, continuous functions, holomorphic functions, trapezoid inequality

Kaynakça

Cerone, P., Dragomir, S. S., Trapezoidal-Type Rules From an Inequalities Point of View, Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou (Ed.), CRC Press, NY, 2000, 65-134.
Cerone, P., Dragomir, S. S., Pearce, C. E. M., A generalised trapezoid inequality for functions of bounded variation, Turkish J. Math., 24(2) (2000), 147-163.
Dragomir, S. S., An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Ineq. Pure & Appl. Math., 3(2) (2002), Art. 31. https://www.emis.de/journals/JIPAM/article183.html?sid=183
Dragomir, S. S., An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Ineq. Pure & Appl. Math., 3(3) (2002), Art. 35. https://www.emis.de/journals/JIPAM/article187.html?sid=187
Dragomir, S. S., The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), 495–508.
Dragomir, S. S., Rassias, Th. M. (Eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht, 2002.
Kechriniotis, A. I., Assimakis, N. D., Generalizations of the trapezoid inequalities based on a new mean value theorem for the remainder in Taylor’s formula, J. Inequal. Pure Appl. Math., 7(3) (2006), Article 90, 13 pp.
Liu, Z., Some inequalities of perturbed trapezoid type, J. Inequal. Pure Appl. Math., 7(2) (2006), Article 47, 9 pp.
Mercer, McD. A., On perturbed trapezoid inequalities, J. Inequal. Pure Appl. Math., 7(4) (2006), Article 118, 7 pp. (electronic).
Ostrowski, A., Uber die absolutabweichung einer differentiierbaren funktion von ihrem integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
Ujevic, N., Error inequalities for a generalized trapezoid rule, Appl. Math. Lett. 19(1) (2006), 32–37.

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Research Article
Yazarlar	Sever Dragomır 0000-0003-2902-6805
Yayımlanma Tarihi	31 Aralık 2021
Gönderilme Tarihi	23 Eylül 2020
Kabul Tarihi	17 Nisan 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

APA	Dragomır, S. (2021). An extension of trapezoid inequality to the complex integral. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 1113-1130. https://doi.org/10.31801/cfsuasmas.798863
AMA	Dragomır S. An extension of trapezoid inequality to the complex integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2021;70(2):1113-1130. doi:10.31801/cfsuasmas.798863
Chicago	Dragomır, Sever. “An Extension of Trapezoid Inequality to the Complex Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 2 (Aralık 2021): 1113-30. https://doi.org/10.31801/cfsuasmas.798863.
EndNote	Dragomır S (01 Aralık 2021) An extension of trapezoid inequality to the complex integral. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 1113–1130.
IEEE	S. Dragomır, “An extension of trapezoid inequality to the complex integral”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 2, ss. 1113–1130, 2021, doi: 10.31801/cfsuasmas.798863.
ISNAD	Dragomır, Sever. “An Extension of Trapezoid Inequality to the Complex Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (Aralık 2021), 1113-1130. https://doi.org/10.31801/cfsuasmas.798863.
JAMA	Dragomır S. An extension of trapezoid inequality to the complex integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:1113–1130.
MLA	Dragomır, Sever. “An Extension of Trapezoid Inequality to the Complex Integral”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 2, 2021, ss. 1113-30, doi:10.31801/cfsuasmas.798863.
Vancouver	Dragomır S. An extension of trapezoid inequality to the complex integral. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):1113-30.