On a functional equation involving iterates and powers

被引：1
作者：
Morawiec, Janusz [1 ]
机构：
[1] Univ Silesia, Inst Math, PL-40007 Katowice, Poland
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2014年
关键词：
iterative functional equation; continuous solution; bijection;
D O I：
10.1186/1687-1847-2014-271
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a complete list of all continuous solutions f: (0,+infinity)->(0,+infinity) of the equation f(2)(x) = gamma[f(x)](alpha)x(beta), where alpha, beta and gamma > 0 are given real numbers. MSC: Primary 39B22; secondary 39B12; 26A18
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页数：10
相关论文
共 32 条
[1]  
Anschuetz R, 1997, COLL MATH J, V27, P388
[2]  
Babbage C., 1815, Philos. Trans. R. Soc. Lond., V105, P389
[3]  
Baron K., 2001, AEQUATIONES MATH, V61, P1, DOI DOI 10.1007/S000100050159
[4]  
Boros Z., 2013, AEQUATIONES MATH, V86, P293
[5]  
Brillouet-Belluot N, 2012, AEQUATIONES MATH, V84, P312
[6]  
Brodsky YS, 1983, FUNCTIONAL EQUATIONS
[7]   Leading coefficient problem for polynomial-like iterative equations [J].
Chen, Jingmin ;
Zhang, Weinian .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 349 (02) :413-419
[8]  
[CHEN Li 陈丽], 2008, [数学研究与评论, Journal of Mathematical Research and Exposition], V28, P323
[9]   When does f-1=1/f? [J].
Cheng, R ;
Dasgupta, A ;
Ebanks, BR ;
Kinch, LF ;
Larson, LM ;
McFadden, RB .
AMERICAN MATHEMATICAL MONTHLY, 1998, 105 (08) :704-717
[10]  
Euler R., 1981, MATH MAG, V54, P185
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