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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 Schur-Convexity of Averages of Convex Functions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 581918 25 pages doi 10.1155 2011 581918 Research Article Schur-Convexity of Averages of Convex Functions Vera Culjak 1 Iva Franjic 2 Roqia Ghulam 3 and Josip PeCariC4 1 Department of Mathematics Faculty of Civil Engineering University of Zagreb KaCiCeva 26 10000 Zagreb Croatia 2 Faculty of Food Technology and Biotechnology University of Zagreb Pierottijeva 6 10000 Zagreb Croatia 3 Abdus Salam School of Mathematical Sciences 68-B New Muslim Town Lahore 54600 Pakistan 4 Faculty of Textile Technology University of Zagreb Prilaz baruna Filipovica 28a 10000 Zagreb Croatia Correspondence should be addressed to Roqia Ghulam rukiyya@gmail.com Received 12 November 2010 Accepted 11 January 2011 Academic Editor Matti K. Vuorinen Copyright 2011 Vera Culjak et al. 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. The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established and some applications of the extended result are given. Furthermore Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally some results on convexity and Schur-convexity involving divided difference are considered. 1. Introduction The property of Schur-convexity and Schur-concavity has invoked the interest of many researchers and numerous papers have been dedicated to the investigation of it. The object of this paper is to present an overview of the results related to the study of Schur-convexity of various means and functions in particular those connected with the
