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 Generalized Heronian Means Involving Two Parameters | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 879273 9 pages doi 2008 879273 Research Article Schur Convexity of Generalized Heronian Means Involving Two Parameters Huan-Nan Shi 1 Mihaly Bencze 2 Shan-He Wu 3 and Da-Mao Li1 1 Department of Electronic Information Teacher s College Beijing Union University Beijing 100011 China 2 Department of Mathematics Aprily Lajos High School Str. Dupa Ziduri 3 500026 Brasov Romania 3 Department of Mathematics and Computer Science Longyan University Longyan Fujian 364000 China Correspondence should be addressed to Shan-He Wu shanhely@ Received 2 September 2008 Accepted 26 December 2008 Recommended by A. Laforgia The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means. Copyright 2008 Huan-Nan Shi 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. 1. Introduction Throughout the paper R denotes the set of real numbers x xi x2 . xn denotes n-tuple n-dimensional real vector the set of vectors can be written as Rn x x1 . . xn xi e R i 1 . n Rn x x1 . . xn xi 0 i 1 . . n n -í Y Ố J I x x1 . xn xi . in j. In particular the notations R R and R denote R1 Rị and Rị respectively. In what follows we assume that a b e Rị. The classical Heronian means of a and b is defined as 1 see also 2 He a b a ab b 3 2 Journal of Inequalities and Applications In 3 an analogue of Heronian means is defined by H a b a 4 ab b 6 Janous 4 presented a weighted generalization of the above Heronian-type means as follows Hw a b a w ãb b -Jab 0 w x w x . w 2 Recently the following exponential generalization of Heronian means was considered by
