Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NEW WEIGHTED OSTROWSKI-GRUSS-CEBYSEV TYPE INEQUALITIES

  • Liu, Wen-Jun (COLLEGE OF MATHEMATICS AND PHYSICS NANJING UNIVERSITY OF INFORMATION SCIENCE AND TECHNOLOGY) ;
  • Huang, Yu (COLLEGE OF MATHEMATICS AND PHYSICS NANJING UNIVERSITY OF INFORMATION SCIENCE AND TECHNOLOGY) ;
  • Pan, Xing-Xia (DEPARTMENT OF CALCULATION AND INFORMATION SCIENCE NANCHANG INSTITUTE OF AERONAUTICAL TECHNOLOGY)
  • Published : 2008.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, by introducing parameter r>1, new weighted Ostrowski-Gruss-Cebysev type inequalities for 1/p+11/q=1-1/r are established.

Keywords

References

  1. P. Cerone, J. Roumeliotis, and G. Hanna, On weighted three point quadrature rules, ANZIAM J. 42 (2000), (C), C340-C361 https://doi.org/10.21914/anziamj.v42i0.602
  2. S. S. Dragomir, P. Cerone, and J. Roumeliotis, A new generalization of Ostrowski's integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett. 13 (2000), no. 1, 19-25
  3. S. S. Dragomia, P. Cerone, J. Roumelitis, and S. Wang, A weighted version of Ostrowski inequality for mappings of Holder type and applications in numerical analysis, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 42(90) (1999), no. 4, 301-314
  4. W. J. Liu, Q. L. Xue, and S. F. Wang, Several new perturbed Ostrowski-like type inequalities, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 4, Article 110, 6 pp
  5. W. J. Liu, Q. L. Xue, and J. W. Dong, New Ostrowski type inequalities involving two functions, J. Appl. Math. & Informatios, 26 (2008), no. 1-2, 291-297
  6. D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993
  7. D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordricht-Boston-London, 1994
  8. B. G. Pachpatte, A note on Ostrowski like inequalities, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Article 114, 4 pp
  9. B. G. Pachpatte, On Ostrowski-Gruss-Cebysev type inequalities for functions whose modulus of derivatives are convex, JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Article 128, 15 pp
  10. A. Rafiq, N. A. Mir, and F. Ahmad, Weighted Ostrowski type inequality for differentiable mappings whose first derivatives belong to Lp(a, b), Gen. Math. 14 (2006), no. 3, 91-102

Cited by

  1. Some Weighted Integral Inequalities with a Parameter and Applications vol.109, pp.2, 2010, https://doi.org/10.1007/s10440-008-9323-2
  2. Asymptotic expressions for error terms of the perturbed mid-point and trapezoid rules vol.15, pp.6, 2012, https://doi.org/10.1080/09720502.2012.10700811
  3. New weighted Ostrowski and Čebyšev type inequalities on time scales vol.60, pp.5, 2010, https://doi.org/10.1016/j.camwa.2010.06.033