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Báo cáo hóa học: " Research Article Solvability and Algorithms for Functional Equations Originating from Dynamic Programming"

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 Solvability and Algorithms for Functional Equations Originating from Dynamic Programming | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 701519 30 pages doi 10.1155 2011 701519 Research Article Solvability and Algorithms for Functional Equations Originating from Dynamic Programming Guojing Jiang 1 Shin Min Kang 2 and Young Chel Kwun3 1 Organization Department Dalian Vocational Technical College Dalian Liaoning 116035 China 2 Department of Mathematics and RINS Gyeongsang National University Jinju 660-701 Republic of Korea 3 Department of Mathematics Dong-A University Pusan 614-714 Republic of Korea Correspondence should be addressed to Young Chel Kwun yckwun@dau.ac.kr Received 5 January 2011 Accepted 11 February 2011 Academic Editor Yeol J. Cho Copyright 2011 Guojing Jiang 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 main purpose of this paper is to study the functional equation arising in dynamic programming of multistage decision processes f x optyeDopt p x y q x y f a x y r x y f b x y s x y f c x y for all x e S. A few iterative algorithms for solving the functional equation are suggested. The existence uniqueness and iterative approximations of solutions for the functional equation are discussed in the Banach spaces BC S and B S and the complete metric space BB S respectively. The properties of solutions nonnegative solutions and nonpositive solutions and the convergence of iterative algorithms for the functional equation and other functional equations which are special cases of the above functional equation are investigated in the complete metric space BB S respectively. Eight nontrivial examples which dwell upon the importance of the results in this paper are also given. 1. Introduction The existence uniqueness and iterative approximations of solutions for several classes of functional equations arising in dynamic programming were