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Báo cáo hóa học: " Research Article Fixed Point Theorems for Random Lower Semi-Continuous Mappings"

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 Fixed Point Theorems for Random Lower Semi-Continuous Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 584178 7 pages doi 10.1155 2009 584178 Research Article Fixed Point Theorems for Random Lower Semi-Continuous Mappings Raul Fierro 1 2 Carlos Martinez 1 and Claudio H. Morales3 1 Instituto de Matematicas Pontificia Universidad Catolica de Valparaiso Cerro Baron Valparaiso Chile 2 Laboratorio de Analisis Estocdstico CIMFAV Universidad de Valparaiso Casilla 5030 Valparaiso Chile 3 Department of Mathematics University of Alabama in Huntsville Huntsville AL 35899 USA Correspondence should be addressed to Claudio H. Morales morales@math.uah.edu Received 31 January 2009 Accepted 1 July 2009 Recommended by Naseer Shahzad We prove a general principle in Random Fixed Point Theory by introducing a condition named P which was inspired by some of Petryshyn s work and then we apply our result to prove some random fixed points theorems including generalizations of some Bharucha-Reid theorems. Copyright 2009 Raul Fierro 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 Let fX d be a metric space and S a closed and nonempty subset of X. Denote by 2X resp. C X the family of all nonempty resp. nonempty and closed subsets of X. A mapping T S 2X is said to satisfy condition P if for every closed ball B of S with radius r 0 and any sequence xn in S for which d xn B 0 and d xn T xnỴ 0 as n TO there exists x0 6 B such that x0 6 T xo where d x B inf d x y y 6 B . If Q is any nonempty set we say that the operator T Q X S 2X satisfies condition P if for each w 6 Q the mapping Tw S 2X satisfies condition P . We should observe that this latter condition is related to a condition that was originally introduced by Petryshyn 1 for single-valued operators in order to prove existence of fixed points. However in our case the .