Some Inequalities for n-Time Differentiable Mappings Using a Multi-Step Kernel with Applications

Main Article Content

Sofian Obeidat


In this paper, we develop a new multi-step kernel and use it to establish new Ostrowski's type inequalities for n-time differentiable mappings, whose n-th derivatives satisfy convexity and quasi-convexity conditions. Applications of our findings to random variables and approximation of integrals are given.

Article Details


  1. P. Cerone, S.S. Dragomir, J. Roumeliotis and J. Sunde, A new generalization of the trapezoid formula for n-time differentiable mappings and applications, Demonstr. Math. 33 (4) (2000), 719-736.
  2. X. L. Cheng, Improvement of some Ostrowski-Gr ¨uss type inequalities, Computers Math. Appl. 42 (2001), 109-114.
  3. L. Chun and F. Qi, Integral inequalities of Hermite-Hadamard type for functions whose third derivatives are convex, J. Inequal. Appl. 2013 (2013), Art. ID 451.
  4. S. S. Dragomir and S. Wang, An inequality of Ostrowski-Gr ¨uss type and its applications to the estimation of error bounds for some special means and for home numerical quadrature rules, Computers Math. Appl. 33 (11) (1997), 15-20.
  5. D. Y. Hwang, Some Inequalities for n-time Differentiable Mappings and Applications, Kyung. Math. J. 43 (2003), 335-343.
  6. J. L. W. V. Jensen, On konvexe funktioner og uligheder mel lem middlvaerdier, Nyt. Tidsskr. Math. B. 16 (1905), 49-69.
  7. A. I. Kechriniotis and Y. A. Theodorou, New integral inequalities for n-time differentiable functions with applications for pdfs, Appl. Math. Sci. 2 (8) (2008), 353-362.
  8. A. Ostrowski, Uber die Absolutabweichung einer differentierbaren Funktion von ihren Integralmittelwert, Comment. Math. Helv., 10 (1938), 226-227.
  9. M. E. Ozdemir and C. Yildiz, A new generalization of the midpoint formula for n-time differentiable mappings which are convex, arXiv:1404.5128v1, 2014.
  10. B.G. Pachpatte, New inequalities of Ostrowski and Trapezoid type for n-time differentiable functions, Bull. Korean Math. Soc. 41 (4) (2004), 633-639.
  11. J. E. Pecaric, F. Proschan, Y.L. Tong, Convex Function, Partial Ordering and Statistical Applications, Academic Press, New York, 1991.
  12. S. H. Wang and F. Qi, Inequalities of Hermite-Hadamard type for convex functions which are n-times differentiable, Math. Inequal. Appl. 16 (4) (2013), 1269-1278.