Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1352-1364.
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Zhiheng Yu1,Xiaobing Gong2,*()
Received:
2018-09-20
Online:
2019-12-26
Published:
2019-12-28
Contact:
Xiaobing Gong
E-mail:xbgong@163.com
Supported by:
CLC Number:
Zhiheng Yu,Xiaobing Gong. Polynomial Solutions of the Polynomial-Like Iterative Equation[J].Acta mathematica scientia,Series A, 2019, 39(6): 1352-1364.
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1 | Becker T, Weispfenning V. Gröbner Basis: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, 1993 |
2 | Bessis D , Marmi S , Turchetti G . On the singularities of divergent majorant series arising from normal form theory. Rend Math Ser, 1989, 9: 645- 659 |
3 | Buchberger B. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem Nulldimensional Polynomideal[D]. Austria: Universität Innsbruck, 1965 |
4 |
Chen X , Shi Y , Zhang W . Planar quadratic degree-preserving maps and their iteration. Results Math, 2009, 55: 39- 63
doi: 10.1007/s00025-009-0389-6 |
5 |
Chen X , Zhang W . Decomposition of algebraic sets and applications to weak centers of cubic systems. J Comput Appl Math, 2009, 232: 565- 581
doi: 10.1016/j.cam.2009.06.029 |
6 |
Chen J , Zhang W . Leading coefficient problem for polynomial-like iterative equations. J Math Anal Appl, 2009, 349: 413- 419
doi: 10.1016/j.jmaa.2008.09.015 |
7 |
Collet P , Eckmann J P , Lanford O E . Universal properties of maps on an interval. Comm Math Phys, 1980, 76: 211- 254
doi: 10.1007/BF02193555 |
8 | Draga S . A note on the polynomial-like iterative equations order. Comment Math, 2016, 56: 243- 249 |
9 |
Draga S , Morawiec J . Reducing the polynomial-like iterative equations order and a generalized Zoltán Boros' problem. Aequationes Math, 2016, 90: 935- 950
doi: 10.1007/s00010-016-0420-4 |
10 |
Fontich E . Transversal homoclinic points of a class of conservative diffeomorphisms. J Diffe Equ, 1990, 87: 1- 27
doi: 10.1016/0022-0396(90)90012-E |
11 | Gelfand I M, Kapranov M M, Zelevinsky A V. Discriminants, Resultantsand Multidimensional Determinants. Boston: Birkhäuser, 1994 |
12 | Gianni P , Trager B , Zacharias G . Gröbner basis and primary decomposition of polynomials. J Symbolic Comput, 1988, 6: 146- 167 |
13 |
Gong X . Convex solutions of the polynomial-like iterative equation on open set. Bull Korean Math Soc, 2014, 51: 641- 651
doi: 10.4134/BKMS.2014.51.3.641 |
14 | Gong X , Zhang P . Convex solutions of the polynomial-like iterative equation with variable coefficents. J Appl Anal Comput, 2016, 6: 306- 321 |
15 |
Gong X , Zhang W . Convex solutions of the polynomial-like iterative equation in Banach spaces. Publ Math Debrecen, 2013, 82: 341- 358
doi: 10.5486/PMD.2013.5305 |
16 |
Greenfield S J , Nussbaum R D . Dynamics of a quadratic map in two complex variables. J Diffe Equ, 2001, 169: 57- 141
doi: 10.1006/jdeq.2000.3895 |
17 |
Jarczyk W . On an equation of linear iteration. Aequationes Math, 1996, 51: 303- 310
doi: 10.1007/BF01833285 |
18 | Kuczma M , Choczewski B , Ger R . Iterative Functional Equations. New York: Cambridge University Press, 1990 |
19 |
Kulczycki M , Tabor J . Iterative functional equations in the class of Lipschitz functions. Aequationes Math, 2002, 64: 24- 33
doi: 10.1007/s00010-002-8028-2 |
20 | Li L , Zhang W . Continuously decreasing solutions for polynomial-like iterative equations. Sci China Ser, 2013, 56A: 1051- 1058 |
21 | Liu J, Duan H, Yu Z. On the blended soltuions of polynomial-like iterative equation with multivalued functions. Discrete Dyn Nat Soc, 2018, Art ID: 9862794 |
22 |
Liu L , Gong X . The polynomial-like iterative equation for PM functions. Sci China Math, 2017, 60: 1503- 1514
doi: 10.1007/s11425-016-0319-x |
23 |
Matkowski J , Zhang W . Method of characteristic for functional equations in polynomial form. Acta Math Sinica, 1997, 13: 421- 432
doi: 10.1007/BF02560023 |
24 |
Matkowski J , Zhang W . Characteristic analysis for a polynomial-like iterative equation. Chinese Sci Bull, 1998, 43: 192- 196
doi: 10.1007/BF02898908 |
25 | Matkowski J , Zhang W . On linear dependence of iterates. J Appl Anal, 2000, 6: 149- 157 |
26 |
McCarthy P J . The general exact bijective continuous solution of Feigenbaum's functional equation. Comm Math Phys, 1983, 91: 431- 443
doi: 10.1007/BF01208784 |
27 |
Nabeya S . On the functional equation $f(p+qx+rf(x))=a+bx+cf(x)$. Aequationes Math, 1974, 11: 199- 211
doi: 10.1007/BF01834919 |
28 |
Ng C T , Zhang W . Invariant curves for planar mappings. J Differ Equ Appl, 1997, 3: 147- 168
doi: 10.1080/10236199708808092 |
29 |
Ng C T , Zhao H . Periodic and continuous soltuions of a polynomial-like iterative equation. Aequationes Math, 2017, 91: 185- 200
doi: 10.1007/s00010-016-0456-5 |
30 | Ritt J F. Differential Algebra. New York: Amer Math Soc, 1950 |
31 | Romanovski V G, Shafer D S. The Center and Cyclicity Problems: a Computational Algebra Approach. Boston: Birkhäuser, 2009 |
32 | 司建国. 迭代方程$\sum\limits_{i = 1}^n {{\lambda _i}f^i(x) = F(x)} $局部解析解的存在性. 数学学报, 1994, 37: 590- 600 |
Si J G . The existence of local analytic solutions of the iterated equations $\sum\limits_{i = 1}^n {{\lambda _i}f^i(x) = F(x)}$. Acta Math Sin (Chinese Series), 1994, 37: 590- 600 | |
33 |
Tabor J , Żołdak M . Iterative equations in Banach spaces. J Math Anal Appl, 2004, 299: 651- 662
doi: 10.1016/j.jmaa.2004.06.011 |
34 |
Tabor J , Tabor J . On a linear iterative equation. Results Math, 1995, 27: 412- 421
doi: 10.1007/BF03322847 |
35 | Targonski G. Topics in Iteration Theory. Göttingen: Vandenhoeck and Ruprecht, 1981 |
36 |
Wu W T . On zeros of algebraic equations-An appliation of Ritt's principle. Chin Sci Bul, 1986, 31: 1- 5
doi: 10.1360/csb1986-31-1-1 |
37 | Xu B , Zhang W . Construction of continuous solutions and stability for the polynomial-like iterative equation. J Math Anal Appl, 2007, 325: 483- 497 |
38 | Xu B , Zhang W . Decreasing solutions and convex solutions of the polynomial-like iterative equation. J Math Anal Appl, 2007, 329: 1160- 1170 |
39 | Xu B , Nikodem K , Zhang W . On a multivalued iterative equation of order $n$. J Convex Anal, 2011, 18: 673- 686 |
40 |
Yang D , Zhang W . Characteristic solutions of polynomial-like iterative equations. Aequationes Math, 2004, 67: 80- 105
doi: 10.1007/s00010-003-2708-4 |
41 |
Yang L , Yang L , Yu Z , Zhang W . Real polynomial iterative roots in the case of nonmonotonicity height $\ge 2$. Sci China Math, 2012, 55: 2433- 2446
doi: 10.1007/s11425-012-4537-1 |
42 |
Yu Z , Yang L , Zhang W . Discussion on polynomials having polynomial iterative roots. J Symb Comput, 2012, 47: 1154- 1162
doi: 10.1016/j.jsc.2011.12.038 |
43 | Zhang J , Yang L , Zhang W . Some advances on functional equations. Adv Math (China), 1995, 24: 385- 405 |
44 |
Zhang W . Discussion on the iterated equation $\sum\limits^{n}_{i=1}\lambda_{i}f^{i}(x)=F(x)$. Chinese Sci Bull, 1987, 32: 1444- 1451
doi: 10.1360/csb1987-32-19-1444 |
45 |
Zhang W . Discussion on the differentiable solutions of the iterated equation $\sum\limits_{i=1}^{n}\lambda_{i}f^{i}(x)=F(x)$. Nonlinear Anal, 1990, 15: 387- 398
doi: 10.1016/0362-546X(90)90147-9 |
46 |
Zhang W . On existence for polynomial-like iterative equations. Results Math, 2004, 45: 185- 194
doi: 10.1007/BF03323006 |
47 |
Zhang W . Solutions of equivariance for a polynomial-like iterative equation. Proc Roy Soc Edinburgh Sect A, 2000, 130: 1153- 1163
doi: 10.1017/S0308210500000615 |
48 |
Zhang W , Baker J A . Continuous solutions of a polynomial-like iterative equation with variable coefficients. Ann Polon Math, 2000, 73: 29- 36
doi: 10.4064/ap-73-1-29-36 |
49 | Zhang W , Zhang W . On continuous solutions of $n$-th order polynomial-like iterative equations. Publ Math Debrecen, 2010, 76 (1/2): 117- 134 |
50 |
Zhang W , Xu B , Zhang W . Global solutions for leading coefficient problem of polynomial-like iterative equations. Results Math, 2013, 63: 79- 93
doi: 10.1007/s00025-011-0162-5 |
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