caa a22 4500 605508429 CHVBK 20210128100636.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-014-0277-3 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0277-3 Smoothness repaired by iteration [Elektronische Daten] [Xiaohua Liu, Liu Liu, Weinian Zhang] It is easy to find some nonsmooth functions whose iterates are smooth ones, showing that iteration can change nonsmoothness into smoothness. In order to investigate the change and avoid complicated computation, in this paper we classify piecewise C 1 self-mappings on the compact interval [0, 1] each of which has only one nonsmooth point. We give necessary and sufficient conditions under which the second order iterates are C 1 smooth functions. Springer Basel, 2014 Iteration nationallicence Nonsmooth nationallicence Piecewise smooth nationallicence Liu Xiaohua Department of Mathematics, Leshan Normal College, 614004, Leshan, Sichuan, People's Republic of China aut Liu Liu Department of Mathematics, Southwest Jiaotong University, 610031, Chengdu, Sichuan, People's Republic of China aut Zhang Weinian Department of Mathematics, Sichuan University, 610064, Chengdu, Sichuan, People's Republic of China aut Aequationes mathematicae Springer Basel 89/3(2015-06-01), 829-848 0001-9054 89:3<829 2015 89 10 https://doi.org/10.1007/s00010-014-0277-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0277-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Xiaohua Department of Mathematics, Leshan Normal College, 614004, Leshan, Sichuan, People's Republic of China aut NATIONALLICENCE 700 1- Liu Liu Department of Mathematics, Southwest Jiaotong University, 610031, Chengdu, Sichuan, People's Republic of China aut NATIONALLICENCE 700 1- Zhang Weinian Department of Mathematics, Sichuan University, 610064, Chengdu, Sichuan, People's Republic of China aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 829-848 0001-9054 89:3<829 2015 89 10