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Year 2019, Volume: 7 Issue: 2, 337 - 343, 15.10.2019

Abstract

References

  • [1] M.W. Alomari and S.S. Dragomir, Various error estimations for several Newton–Cotes quadrature formulae in terms of at most first derivative and applications in numericaal integration, Jordan J. Math. & Stat., 7 (2) 2014, 89–108.
  • [2] M.W. Alomari, A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation, Preprint, RGMIA Res. Rep. Coll., 14 (2011), article87. [http://ajmaa.org/RGMIA/v14.php]
  • [3] M.W. Alomari, A companion of Dragomir’s generalization of Ostrowski’s inequality and applications in numerical integration, Ukrainian Math. J., 64 (4) (2012), 491–510
  • [4] H. Budak, F. Usta and M.Z. Sarikaya, New upper bounds of ostrowski type integral inequalities utilizing Taylor expansion, Hacettepe Journal of Mathematics and Statistics, 47 (3) (2018), 567–578.
  • [5] H. Budak, F. Usta, M.Z. Sarikaya and M.E. Ozdemir, On generalization of midpoint type inequalities with generalized fractional integral operators, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113(2) (2019), 769–790.
  • [6] A. Ostrowski, U¨ ber die absolutabweichung einer differentiiebaren funktion vonihrem integralmittelwert, Comment. Math. Helv., 10 (1938) 226–227.
  • [7] Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999) 495–508.
  • [8] S.S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, RGMIA Preprint, Vol. 5 Supp. (2002) article No. 28. [http://ajmaa.org/RGMIA/papers/v5e/COIFBVApp.pdf]
  • [9] A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Th., 115 (2002), 260–288.
  • [10] K.L. Tseng, S.R. Hwang, S.S. Dragomir, Generalizations of weighted Ostrowski type inequalities for mappings of bounded variation and their applications, Computers and Mathematics with Applications, 55 (2008) 1785–1793.
  • [11] K.L. Tseng, Improvements of some inequalites of Ostrowski type and their applications, Taiwanese J. Math., 12(9) (2008), 2427–2441.
  • [12] K.L. Tseng, S.R. Hwang, G.S. Yang and Y.M. Chou, Improvements of the Ostrowski integral inequality for mappings of bounded variation I, Appl. Math. Comp., 217 (2010) 2348–2355.
  • [13] F. Usta, H. Budak, M.Z. Sarikaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat 32 (6), 2153–2171
  • [14] F. Usta, H. Budak and M.Z. Sarikaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113 (2) (2019), 1059–1080.

A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation

Year 2019, Volume: 7 Issue: 2, 337 - 343, 15.10.2019

Abstract

A weighted companion of Ostrowski--Midpoint type inequality is established. Application to a composite quadrature rule is provided.

References

  • [1] M.W. Alomari and S.S. Dragomir, Various error estimations for several Newton–Cotes quadrature formulae in terms of at most first derivative and applications in numericaal integration, Jordan J. Math. & Stat., 7 (2) 2014, 89–108.
  • [2] M.W. Alomari, A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation, Preprint, RGMIA Res. Rep. Coll., 14 (2011), article87. [http://ajmaa.org/RGMIA/v14.php]
  • [3] M.W. Alomari, A companion of Dragomir’s generalization of Ostrowski’s inequality and applications in numerical integration, Ukrainian Math. J., 64 (4) (2012), 491–510
  • [4] H. Budak, F. Usta and M.Z. Sarikaya, New upper bounds of ostrowski type integral inequalities utilizing Taylor expansion, Hacettepe Journal of Mathematics and Statistics, 47 (3) (2018), 567–578.
  • [5] H. Budak, F. Usta, M.Z. Sarikaya and M.E. Ozdemir, On generalization of midpoint type inequalities with generalized fractional integral operators, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113(2) (2019), 769–790.
  • [6] A. Ostrowski, U¨ ber die absolutabweichung einer differentiiebaren funktion vonihrem integralmittelwert, Comment. Math. Helv., 10 (1938) 226–227.
  • [7] Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999) 495–508.
  • [8] S.S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, RGMIA Preprint, Vol. 5 Supp. (2002) article No. 28. [http://ajmaa.org/RGMIA/papers/v5e/COIFBVApp.pdf]
  • [9] A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Th., 115 (2002), 260–288.
  • [10] K.L. Tseng, S.R. Hwang, S.S. Dragomir, Generalizations of weighted Ostrowski type inequalities for mappings of bounded variation and their applications, Computers and Mathematics with Applications, 55 (2008) 1785–1793.
  • [11] K.L. Tseng, Improvements of some inequalites of Ostrowski type and their applications, Taiwanese J. Math., 12(9) (2008), 2427–2441.
  • [12] K.L. Tseng, S.R. Hwang, G.S. Yang and Y.M. Chou, Improvements of the Ostrowski integral inequality for mappings of bounded variation I, Appl. Math. Comp., 217 (2010) 2348–2355.
  • [13] F. Usta, H. Budak, M.Z. Sarikaya and E. Set, On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat 32 (6), 2153–2171
  • [14] F. Usta, H. Budak and M.Z. Sarikaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 113 (2) (2019), 1059–1080.
There are 14 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mohammad W. Alomari 0000-0002-6696-9119

Publication Date October 15, 2019
Submission Date January 5, 2019
Acceptance Date May 16, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Alomari, M. W. (2019). A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation. Konuralp Journal of Mathematics, 7(2), 337-343.
AMA Alomari MW. A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation. Konuralp J. Math. October 2019;7(2):337-343.
Chicago Alomari, Mohammad W. “A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation”. Konuralp Journal of Mathematics 7, no. 2 (October 2019): 337-43.
EndNote Alomari MW (October 1, 2019) A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation. Konuralp Journal of Mathematics 7 2 337–343.
IEEE M. W. Alomari, “A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation”, Konuralp J. Math., vol. 7, no. 2, pp. 337–343, 2019.
ISNAD Alomari, Mohammad W. “A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation”. Konuralp Journal of Mathematics 7/2 (October 2019), 337-343.
JAMA Alomari MW. A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation. Konuralp J. Math. 2019;7:337–343.
MLA Alomari, Mohammad W. “A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation”. Konuralp Journal of Mathematics, vol. 7, no. 2, 2019, pp. 337-43.
Vancouver Alomari MW. A Weighted Companion of Ostrowski-Midpoint Inequality for Mappings of Bounded Variation. Konuralp J. Math. 2019;7(2):337-43.
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