Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Ostrowski Type Inequalities for Higher-Order Derivatives | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 162689 8 pages doi 2009 162689 Research Article Ostrowski Type Inequalities for Higher-Order Derivatives Mingjin Wang1 and Xilai Zhao2 1 Department of Applied Mathematics Jiangsu Polytechnic University Changzhou 213164 Jiangsu China 2 Department of Mechanical and Electrical Engineering Hebi College of Vocation and Technology Hebi Henan 458030 China Correspondence should be addressed to Mingjin Wang wang197913@ Received 12 February 2009 Revised 16 May 2009 Accepted 14 July 2009 Recommended by Patricia J. Y. Wong This paper has shown some new Ostrowski type inequalities involving higher-order derivatives. The results generalized the Ostrowski type inequalities. Applications of the inequalities are also given. Copyright 2009 M. Wang and X. Zhao. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Main Result and Introduction The following inequality is well known in literature as Ostrowski s integral inequality. Let f a b R be continuous on a b and differentiable on a b whose derivative f a b R is bounded on a b that is Ilf L supie ab f f TO. Then f x - c b f t dt J a x - a b 2 2 b - a 2 b- a f IL 1 b - a Moreover the constant 1 4 is the best possible. Because Ostrowski s integral inequality is useful in some fields many generalizations extensions and variants of this inequality have appeared in the literature see 1-9 and the references given therein. The main aim of this paper is to establish some new Ostrowski type inequalities involving higher-order derivatives. The analysis used in the proof is elementary. The main result of this paper is the following inequality. 2 Journal of Inequalities and Applications Theorem . Suppose 1 f a b R to be continuous on a b 2 f a b R to be nth order .
