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Ostrowski's Type Inequalities for the Complex Integral on Paths

Yıl 2020, Cilt: 3 Sayı: 4, 125 - 138, 01.12.2020
https://doi.org/10.33205/cma.798861

Öz

In this paper we extend the Ostrowski inequality to the integral with respect to arc-length by providing upper bounds for the quantity

|f(v)ℓ(γ)-∫_{γ}f(z)|dz||

under the assumptions that γ is a smooth path parametrized by z(t), t∈[a,b] with the length ℓ(γ), u=z(a), v=z(x) with x∈(a,b) and w=z(b) while f is holomorphic in G, an open domain and γ⊂G. An application for circular paths is also given.

Several applications for circular paths and for some special functions of interest such as the exponential functions are also provided.

Kaynakça

  • S. S. Dragomir: A refinement of Ostrowski's inequality for absolutely continuous functions whose derivatives belong to $L_{\infty }$ and applications. Libertas Math. 22 (2002), 49--63.
  • S. S. Dragomir: A refinement of Ostrowski's inequality for absolutely continuous functions and applications. Acta Math. Vietnam 27 (2002), no. 2, 203--217.
  • S. S. Dragomir: A functional generalization of Ostrowski inequality via Montgomery identity. Acta Math. Univ. Comenian. (N.S.) 84 (2015), no. 1, 63--78. Preprint RGMIA Res. Rep. Coll. 16 (2013), Art. 65, pp. 15 [Online http://rgmia.org/papers/v16/v16a65.pdf].
  • S. S. Dragomir: Ostrowski type inequalities for Lebesgue integral: a survey of recent results. Aust. J. Math. Anal. Appl. 14 (2017), no. 1, Art. 1, 283 pp.
  • S. S. Dragomir: An extension of Ostrowski's inequality to the complex integral}. Preprint RGMIA Res. Rep. Coll. 18 (2018), Art. 112, 17 pp. [Online https://rgmia.org/papers/v21/v21a112.pdf].
  • S. S. Dragomir, S. Wang: Applications of Ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules. Appl. Math. Lett. 11 (1) (1998), 105-109.
  • D. S. Mitrinovi\'{c}, J. E. Pe\v{c}ari\'{c} and A. M. Fink: Inequalities for Functions and Their Integrals and Derivatives. Kluwer Academic Publishers, Dordrecht, 1994.
  • A. Ostrowski: \"{U}ber die Absolutabweichung einerdifferentiierbaren Funktion von ihrem Integralmittelwert}. Comment. Math. Helv. 10 (1938), 226-227.
Yıl 2020, Cilt: 3 Sayı: 4, 125 - 138, 01.12.2020
https://doi.org/10.33205/cma.798861

Öz

Kaynakça

  • S. S. Dragomir: A refinement of Ostrowski's inequality for absolutely continuous functions whose derivatives belong to $L_{\infty }$ and applications. Libertas Math. 22 (2002), 49--63.
  • S. S. Dragomir: A refinement of Ostrowski's inequality for absolutely continuous functions and applications. Acta Math. Vietnam 27 (2002), no. 2, 203--217.
  • S. S. Dragomir: A functional generalization of Ostrowski inequality via Montgomery identity. Acta Math. Univ. Comenian. (N.S.) 84 (2015), no. 1, 63--78. Preprint RGMIA Res. Rep. Coll. 16 (2013), Art. 65, pp. 15 [Online http://rgmia.org/papers/v16/v16a65.pdf].
  • S. S. Dragomir: Ostrowski type inequalities for Lebesgue integral: a survey of recent results. Aust. J. Math. Anal. Appl. 14 (2017), no. 1, Art. 1, 283 pp.
  • S. S. Dragomir: An extension of Ostrowski's inequality to the complex integral}. Preprint RGMIA Res. Rep. Coll. 18 (2018), Art. 112, 17 pp. [Online https://rgmia.org/papers/v21/v21a112.pdf].
  • S. S. Dragomir, S. Wang: Applications of Ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules. Appl. Math. Lett. 11 (1) (1998), 105-109.
  • D. S. Mitrinovi\'{c}, J. E. Pe\v{c}ari\'{c} and A. M. Fink: Inequalities for Functions and Their Integrals and Derivatives. Kluwer Academic Publishers, Dordrecht, 1994.
  • A. Ostrowski: \"{U}ber die Absolutabweichung einerdifferentiierbaren Funktion von ihrem Integralmittelwert}. Comment. Math. Helv. 10 (1938), 226-227.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Sever Dragomır 0000-0003-2902-6805

Yayımlanma Tarihi 1 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 4

Kaynak Göster

APA Dragomır, S. (2020). Ostrowski’s Type Inequalities for the Complex Integral on Paths. Constructive Mathematical Analysis, 3(4), 125-138. https://doi.org/10.33205/cma.798861
AMA Dragomır S. Ostrowski’s Type Inequalities for the Complex Integral on Paths. CMA. Aralık 2020;3(4):125-138. doi:10.33205/cma.798861
Chicago Dragomır, Sever. “Ostrowski’s Type Inequalities for the Complex Integral on Paths”. Constructive Mathematical Analysis 3, sy. 4 (Aralık 2020): 125-38. https://doi.org/10.33205/cma.798861.
EndNote Dragomır S (01 Aralık 2020) Ostrowski’s Type Inequalities for the Complex Integral on Paths. Constructive Mathematical Analysis 3 4 125–138.
IEEE S. Dragomır, “Ostrowski’s Type Inequalities for the Complex Integral on Paths”, CMA, c. 3, sy. 4, ss. 125–138, 2020, doi: 10.33205/cma.798861.
ISNAD Dragomır, Sever. “Ostrowski’s Type Inequalities for the Complex Integral on Paths”. Constructive Mathematical Analysis 3/4 (Aralık 2020), 125-138. https://doi.org/10.33205/cma.798861.
JAMA Dragomır S. Ostrowski’s Type Inequalities for the Complex Integral on Paths. CMA. 2020;3:125–138.
MLA Dragomır, Sever. “Ostrowski’s Type Inequalities for the Complex Integral on Paths”. Constructive Mathematical Analysis, c. 3, sy. 4, 2020, ss. 125-38, doi:10.33205/cma.798861.
Vancouver Dragomır S. Ostrowski’s Type Inequalities for the Complex Integral on Paths. CMA. 2020;3(4):125-38.