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 On Functional Inequalities Originating from Module Jordan Left Derivations | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 278505 9 pages doi 2008 278505 Research Article On Functional Inequalities Originating from Module Jordan Left Derivations Hark-Mahn Kim 1 Sheon-Young Kang 2 and Ick-Soon Chang3 1 Department of Mathematics Chungnam National University Daejeon 305-764 South Korea 2 Department of Industrial Mathematics National Institute for Mathematical Sciences Daejeon 305-340 South Korea 3 Department of Mathematics Mokwon University Daejeon 302-729 South Korea Correspondence should be addressed to Ick-Soon Chang ischang@ Received 18 February 2008 Revised 1 May 2008 Accepted 19 May 2008 Recommended by Andras Rontó We first examine the generalized Hyers-Ulam stability of functional inequality associated with module Jordan left derivation resp. module Jordan derivation . Secondly we study the functional inequality with linear Jordan left derivation resp. linear Jordan derivation mapping into the Jacobson radical. Copyright 2008 Hark-Mahn Kim 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 and Preliminaries Let A be an algebra over the real or complex field F and let M a left A-module resp. A-bimodule . An additive mapping d A M is said to be a module left derivation resp. module derivation if d xy xd y yd x resp. d xy xd y d x y holds for all x y A. An additive mapping d A M is called a module Jordan left derivation resp. module Jordan derivation if d x2 2xd x resp. d x2 xd x d x x is fulfilled for all x A. Since A is a left A-module resp. A-bimodule with the product giving the module multiplication resp. two module multiplications the module left derivation resp. module derivation d A A is a ring left derivation resp. ring derivation and the module Jordan left derivation resp. module .
