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Ostrowski's Type Inequalities for the Complex Integral on Paths

Year 2020, Volume: 3 Issue: 4, 125 - 138, 01.12.2020

Sever Dragomır

https://doi.org/10.33205/cma.798861
Cited By: 1

Abstract

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.

Keywords

Complex integral Ostrowski inequality Integrals on the paths

References

  • 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.

Year 2020, Volume: 3 Issue: 4, 125 - 138, 01.12.2020

Sever Dragomır

https://doi.org/10.33205/cma.798861
Cited By: 1

Abstract

References

  • 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.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sever Dragomır 0000-0003-2902-6805

Publication Date December 1, 2020
Published in Issue Year 2020 Volume: 3 Issue: 4

Cite

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. December 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, no. 4 (December 2020): 125-38. https://doi.org/10.33205/cma.798861.
EndNote Dragomır S (December 1, 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, vol. 3, no. 4, pp. 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 (December 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, vol. 3, no. 4, 2020, pp. 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.

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