##### Title: New Weighted Ostrowski Type Inequalities for Mappings Whose nth Derivatives Are of Bounded Variation

##### Pages: 71-79

##### Cite as:

Huseyin Budak, Samet Erden, M. Zeki Sarikaya, New Weighted Ostrowski Type Inequalities for Mappings Whose nth Derivatives Are of Bounded Variation, Int. J. Anal. Appl., 12 (1) (2016), 71-79.#### Abstract

We establish a new generalization of weighted Ostrowski type inequality for mappings of bounded variation. Spacial cases of this inequality reduce some well known inequalities. With the help of obtained inequality, we give applications for the $k$th moment of random variables.

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#### References

- M. W. Alomari, A Generalization of Weighted Companion of Ostrowski Integral Inequality for Mappings of Bounded Variation, RGMIA Research Report Collection, 14 (2011), Art. ID 87.
- M. W. Alomari and M. A. Latif, Weighted Companion for the Ostrowski and the Generalized Trapezoid Inequalities for Mappings of Bounded Variation, RGMIA Research Report Collection, 14 (2011), Art. ID 92.
- M. W. Alomari and S. S. Dragomir, Mercer–Trapezoid rule for the Riemann–Stieltjes integral with applications, Journal of Advances in Mathematics, 2 (2) (2013), 67–85.
- N. S. Barnett, P. Cerone, S. S. Dragomir and J. Roumeliotis, Some inequalities for the dispersion of a random variable whose pdf is defined on a finite interval, J. Ineq. Pure Appl. Math., 2 (1) (2001), 1–18.
- H. Budak and M. Z. Sarıkaya, On generalization of Dragomir’s inequalities, RGMIA Research Report Collection, 17 (2014), Art. ID 155.
- H. Budak and M. Z. Sarıkaya, New weighted Ostrowski type inequalities for mappings with first derivatives of bounded variation, RGMIA Research Report Collection, 18 (2015), Art. ID 43.
- H. Budak and M. Z. Sarikaya, A new generalization of Ostrowski type inequality for mappings of bounded variation, RGMIA Research Report Collection, 18 (2015), Art. ID 47.
- H. Budak and M. Z. Sarikaya, On generalization of weighted Ostrowski type inequalities for functions of bounded variation, RGMIA Research Report Collection, 18 (2015), Art. ID 51.
- H. Budak and M. Z. Sarikaya, A new Ostrowski type inequality for functions whose first derivatives are of bounded variation, Moroccan Journal of Pure and Applied Analysis, 2 (1) (2016), 1-11.
- H. Budak and M. Z. Sarikaya, A companion of Ostrowski type inequalities for mappings of bounded variation and some applications, RGMIA Research Report Collection, 19 (2016), Art. ID 24, 10.
- H. Budak, M. Z. Sarikaya and A. Qayyum, Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and application, RGMIA Research Report Collection, 19 (2016), Art. ID 25.
- P. Cerone and S. S. Dragomir, On some inequalities for the expectation and variance, Korean J. Comp. & Appl. Math., 8 (2) (2000), 357–380.
- S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bulletin of the Australian Mathematical Society, 60 (1) (1999), 495-508.
- S. S. Dragomir, On the Ostrowski’s integral inequality for mappings with bounded variation and applications, Mathematical Inequalities & Applications, 4 (1) (2001), 59–66.
- S. S. Dragomir, A companion of Ostrowski’s inequality for functions of bounded variation and applications, Inter- national Journal of Nonlinear Analysis and Applications, 5 (1) (2014), 89-97.
- S. S. Dragomir, Some perturbed Ostrowski type inequalities for functions of bounded variation, RGMIA Research Report Collection, 16 (2013), Art. ID 93.
- S. S. Dragomir, Approximating real functions which possess nth derivatives of bounded variation and applications, Computers and Mathematics with Applications, 56 (2008), 2268–2278.
- P. Kumar, Moments inequalities of a random variable defined over a finite interval, J. Inequal. Pure and Appl. Math., 3 (2002), article ID 41.
- W. Liu and Y. Sun, A Refinement of the Companion of Ostrowski inequality for functions of bounded variation and Applications, arXiv:1207.3861v1, (2012).
- Z. Liu, Another generalization of weighted Ostrowski type inequality for mappings of bounded variation, Applied Mathematics Letters, 25 (2012), 393–397.
- Z. Liu, Some Ostrowski type inequalities, Mathematical and Computer Modelling, 48 (2008), 949–960.
- A. M. Ostrowski, ¨ Uber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv., 10 (1938), 226-227.
- J. Roumeliotis, P. Cerone and S. S. Dragomir, An Ostrowski Type Inequality for Weighted Mapping with Bounded Second Derivatives, J. Korean Soc. Ind. Appl. Math., 3(2) (1999), 107-119.
- K-L.Tseng, G-S. Yang, and S. S. Dragomir, Generalizations of Weighted Trapezoidal Inequality for Mappings of Bounded Variation and Their Applications, Mathematical and Computer Modelling, 40 (2004), 77-84.
- K-L. Tseng, Improvements of some inequalites of Ostrowski type and their applications, Taiwan. J. Math., 12 (9) (2008), 2427–2441.
- K-L. Tseng,S-R. Hwang, G-S. Yang, and Y-M. Chou, Weighted Ostrowski Integral Inequality for Mappings of Bounded Variation, Taiwanese J. of Math., 15 (2011), 573-585.