Kerékjártó[1, pp. 224—226] showed that every periodic self-homeomorphism of a disk is topologically conjugate to either a rotation or a reflection, which is restated by Brechner in Ref. [2]. According ...Kerékjártó[1, pp. 224—226] showed that every periodic self-homeomorphism of a disk is topologically conjugate to either a rotation or a reflection, which is restated by Brechner in Ref. [2]. According to this conclusion, every orientation-preserving periodic selfhomeomorphism of a disk must be topologically conjugate to some rotation with a turning range 2kπ/m radian (where m and k are relatively prime positive integers, m≥k), and every orientation-reversing periodic self-homeomorphism of a disk must be topologically con-展开更多
Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this ...Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. （China） 24 （1995） 385-405] （or [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 （2000） 29-36]）.展开更多
文摘Kerékjártó[1, pp. 224—226] showed that every periodic self-homeomorphism of a disk is topologically conjugate to either a rotation or a reflection, which is restated by Brechner in Ref. [2]. According to this conclusion, every orientation-preserving periodic selfhomeomorphism of a disk must be topologically conjugate to some rotation with a turning range 2kπ/m radian (where m and k are relatively prime positive integers, m≥k), and every orientation-reversing periodic self-homeomorphism of a disk must be topologically con-
基金supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LY18A010017the National Science Foundation of China(11101105,11301226)
文摘Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. （China） 24 （1995） 385-405] （or [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 （2000） 29-36]）.
