Cui, Yujun; Zhang, Xingqiu Fixed points for discontinuous monotone operators. (English) Zbl 1197.47068 Fixed Point Theory Appl. 2010, Article ID 926209, 11 p. (2010). The authors obtain some existence theorems of the maximal and minimal fixed points for increasing operators on an order interval in an ordered topological space. An application to differential equations is also given. Reviewer: Ioan A. Rus (Cluj-Napoca) Cited in 1 Document MSC: 47H10 Fixed-point theorems 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 47N20 Applications of operator theory to differential and integral equations Keywords:ordered topological space; increasing operator; monotone iterations; differential equation PDFBibTeX XMLCite \textit{Y. Cui} and \textit{X. Zhang}, Fixed Point Theory Appl. 2010, Article ID 926209, 11 p. (2010; Zbl 1197.47068) Full Text: DOI EuDML References: [1] Guo DJ, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, New York, NY, USA; 1988:viii+275. · Zbl 0661.47045 [2] Amann H: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces.SIAM Review 1976,18(4):620-709. 10.1137/1018114 · Zbl 0345.47044 · doi:10.1137/1018114 [3] Sun J, Zhao Z: Fixed point theorems of increasing operators and applications to nonlinear integro-differential equations with discontinuous terms.Journal of Mathematical Analysis and Applications 1993,175(1):33-45. 10.1006/jmaa.1993.1149 · Zbl 0779.47041 · doi:10.1006/jmaa.1993.1149 [4] Heikkilä S, Lakshmikantham V: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics. Volume 181. Marcel Dekker, New York, NY, USA; 1994:xii+514. · Zbl 0804.34001 [5] Lakshmikantham V, Leela S: Differential and Integral Inequalities. Academic Press, New York, NY, USA; 1969. · Zbl 0177.12403 [6] Klin-eam, C.; Suantai, S., Strong convergence of monotone hybrid method for maximal monotone operators and hemirelatively nonexpansive mappings, No. 2009, 18-14 (2009) · Zbl 1186.47067 [7] Plubtieng, S.; Sriprad, W., An extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces, No. 2009, 16-16 (2009) · Zbl 1186.47076 [8] Krasnosel’skii MA, Lusnikov AB: Regular fixed points and stable invariant sets of monotone operators.Applied Functional Analysis 1996,30(3):174-183. 10.1007/BF02509504 · Zbl 0881.47029 · doi:10.1007/BF02509504 [9] Chen Y-Z: Fixed points for discontinuous monotone operators.Journal of Mathematical Analysis and Applications 2004,291(1):282-291. 10.1016/j.jmaa.2003.11.003 · Zbl 1062.47049 · doi:10.1016/j.jmaa.2003.11.003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.