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 Some Characteristic Quantities Associated with Homogeneous P-Type and M-Type Functions | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 84146 10 pages doi 2007 84146 Research Article Some Characteristic Quantities Associated with Homogeneous P-Type and M-Type Functions Ya-Ping Fang Nan-Jing Huang and Yeol Je Cho Received 22 November 2006 Accepted 20 March 2007 Recommended by Patricia J. Y. Wong Several characteristic quantities associated with homogeneous P-type and M-type functions are introduced and studied in this paper. Further the concepts of P-property and M-property for a couple of functions are introduced and some quantities for a pair of homogeneous functions having P-property and M-property are obtained respectively. As an application a bound for the solution of the homogeneous complementarity problem with a P-type function is derived. Copyright 2007 Ya-Ping Fang 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 For any given P-matrix 1 see also 2-4 M e Rnxn Mathias and Pang 5 introduced a quantity a M by a M min maxXi Mx i. HxU 11 i n In terms of a M a bound for the solution of the linear complementarity problem LCP M q see 2-4 with a P-matrix M is established in 5 . Recently Xiu and Zhang 6 further gave some new properties of a M and introduced a new quantity h M which is defined by ỊỈ M max maxXi Mx ị. xU 11 i n 2 Journal of Inequalities and Applications Moreover Xiu andZhang 6 introduced a fundamental quantity a A B associated with a pair A B having v-column P-property see 2-4 7 by a A B min max Ax i Bx i l x L 11 i n where A B e Rmxn. They developed some characteristic quantities of a A B . By means of these quantities Xiu and Zhang 6 established global error bounds for the vertical and horizontal linear complementarity problems. Motivated by these works in this paper we introduce the .
