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Báo cáo hóa học: " Research Article Random Periodic Point and Fixed Point Results for Random Monotone Mappings in Ordered "

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 Random Periodic Point and Fixed Point Results for Random Monotone Mappings in Ordered | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 723216 13 pages doi 10.1155 2010 723216 Research Article Random Periodic Point and Fixed Point Results for Random Monotone Mappings in Ordered Polish Spaces Xing-Hua Zhu and Jian-Zhong Xiao College of Mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 China Correspondence should be addressed to Jian-Zhong Xiao xiaojz@nuist.edu.cn Received 5 November 2010 Accepted 24 December 2010 Academic Editor M. de la Sen Copyright 2010 X.-H. Zhu and J.-Z. Xiao. 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 measurability of order continuous random mappings in ordered Polish spaces is studied. Using order continuity some random fixed point theorems and random periodic point theorems for increasing decreasing and mixed monotone random mappings are presented. 1. Introduction and Preliminaries The study of random fixed points forms a central topic in probabilistic functional analysis. It was initiated by Spacek 1 Hans 2 and Wang 3 . Some random fixed point theorems play an important role in the theory of random differential and random integral equations see Bharucha-Reid 4 5 . Since the recent 30 years many interesting random fixed point theorems and applications have been developed for example see Beg and Shahzad 6 7 Beg and Abbas 8 Chang 9 Ding 10 Fierro et al. 11 Itoh 12 Li and Duan 13 O Regan et al. 14 Xiao and Tao 15 Xu 16 and Zhu and Xu 17 . In 1976 Caristi 18 introduced a partial ordering in metric spaces by a function and proved the famous Caristi fixed point theorem which is one of the most important results in nonlinear analysis. From then on there appeared many papers concerning fixed point theory and abstract monotone iterative technique in ordered metric spaces or ordered