Wei SONG
,
Lin LI
. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION[J]. Acta mathematica scientia, Series B, 2018
, 38(1)
: 177
-186
.
DOI: 10.1016/S0252-9602(17)30125-X
[1] Agarwal R P, Xu B, Zhang W N. Stability of functional equations in single variable. J Math Anal Appl, 2003, 288:852-869
[2] Baron K, Jarczyk W. Recent results on functional equations in a single variable. Aequat Math, 2001, 61:1-48
[3] Chen J M, Li L. Existence of continuous solutions and stability for a general iterative functional equation. J Comput Appl Math, 2014, 260:509-518
[4] Chen J M, Zhang W N. Leading coefficient problem for polynomial-like iterative equations. J Math Anal Appl, 2009, 349:413-419
[5] Jarczyk W. On an equation of linear iteration. Aequat Math, 1996, 51:303-310
[6] Kuczma M, Choczewski B, Ger R. Iterative Functional Equations, Ecyclopedia of Mathematics and its Application. Cambridge:Cambridge University Press, 1990
[7] Kulczycki M, Tabor J. Iterative functional equations in the class of Lipschitz functions. Aequat Math, 2002, 64:24-33
[8] Li L, Song W. Global solutions for leading coefficient problem of a general iterative equation. Results Math, 2015, 68:247-260
[9] Li L, Zhang W N. Construction of usc solutions for a multivalued iterative equation of order n. Results Math, 2012, 62:203-216
[10] Li L, Zhang W M. Continuously decreasing solutions for polynomial-like iterative equations. Sci China Math, 2013, 56:1051-1058
[11] Li X P, Deng S F. Differentiability for the high dimensional polynomial-like iterative equation. Acta Math Sci, 2005, 25B(1):130-136
[12] Mai J H, Liu X H. Existence, uniqueness and stability of Cm solutions of iterative equations. Sci China Math, 2000, 43:897-913
[13] Malenica M. On the solutions of the functional equation φ(x)+φ2(x)=F(x). Mat Vesnik, 1982, 6:301-305
[14] Nikodem K, Zhang W N. On a multivalued iterative equation. Publ Math Debrecen, 2004, 64:427-435
[15] Si J G. Existence of locally analytic solutions of the iterated equation ∑i=1nλifi(x)=F(x). Acta Math Sin, 1994, 37:590-600(in Chinese)
[16] Tabor J, Tabor J. On a linear iterative equation. Results Math, 1995, 27:412-421
[17] Tabor J, Zoldak M. Iterative equations in Banach spaces. J Math Anal Appl, 2004, 299:651-662
[18] Xu B, Nikodem K, Zhang W N. On a multivalued iterative equation of order n. J Convex Anal, 2011, 3:673-686
[19] Xu B, Zhang W N. Construction of continuous solutions and stability for the polynomial-like iterative equation. J Math Anal Appl, 2007, 325:1160-1170
[20] Xu B, Zhang W N. Decreasing solutions and convex solutions of the polynomial-like iterative equation. J Math Anal Appl, 2007, 329:483-497
[21] Zhang J Z, Yang L, Zhang W N. Some advances on functional equations. Adv Math (China), 1995, 24:385-405
[22] Zhang W N. Discussion on the differentiable solutions of the iterated equation ∑i=1nλifi(x)=F(x). Nonlinear Anal, 1990, 15:387-398
[23] Zhang W N. On existence for polynomial-like iterative equations. Results Math, 2004, 45:185-194
[24] Zhang W N, Baker J A. Continuous solutions of a polynomial-like iterative equation with variable coefficients. Ann Polon Math, 2000, 73:29-36
[25] Zhang W M, Xu B, Zhang W N. Global solutions for leading coefficient problem of polynomial-like iterative equations. Results Math, 2013, 63:79-93
[26] Zhang W X, Xu B. Hyers-Ulum-Rassias stability for a multivalued iterative equation. Acta Math Sci, 2008, 28B(1):54-62
