tailieunhanh - Báo cáo hóa học: "Research Article On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions"

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 Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 230414 11 pages doi 2009 230414 Research Article On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions Krzysztof Cieplinski and Marek Cezary Zdun Institute of Mathematics Pedagogical University Podchorạiych 2 30-084 Kraków Poland Correspondence should be addressed to Krzysztof Cieplinski kc@ Received 23 December 2008 Accepted 24 June 2009 Recommended by Lech Gorniewicz We investigate the existence and uniqueness of solutions p I J of the functional equation p f x F x x e I where I J are closed intervals and f I I F J J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result. Copyright 2009 K. Cieplifiski and M. C. Zdun. 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 Let I a b J c d be closed bounded and nondegenerate . neither of them consists of a single point real intervals and let f I I F J J be continuous functions. The aim of this paper is to discuss under some additional assumptions on the maps f and F the problem of topological conjugacy of f and F. More precisely we investigate the existence and uniqueness of solutions p I J of the following functional equation p f x F y x x e I. Let us recall that a homeomorphism Ự I J satisfying is said to be a topological conjugacy between f and F f and F are then called topologically conjugate whereas an arbitrary function Ự I J fulfilling is called a conjugacy between them so the conjugacy needs not to be continuous surjective or injective . A continuous function f I I is said to be a horseshoe map see 1 if there exist an integer n 1 and a sequence fi 0 of reals such that a to fl tn b 2 Fixed Point Theory and Applications and