p. 39 - 42 On square iterative roots of multifunctions Zhijie Nan and Lin Li Received: May 21, 2009; Revised: December 12, 2010; Accepted: December 17, 2010 Abstract. Most known results on iterative roots are given under the assumption of continuity and monotonicity. In 2009, Li, Jarczyk, Jarczyk and Zhang considered the existence of square iterative roots for multifunctions with exactly one set-valued point. They gave a full description of these roots for strictly monotone, upper semicontinuous multifunctions. In this paper, we investigate the square roots of multifunctions without monotonicity. Keywords: Iterative root; multifunction; monotonicity AMS Subject classification: Primary: 39B12, 37E05, 54C60 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |