TY - JOUR
T1 - Recurrence equations over trees in a non-Archimedean context
AU - Mukhamedov, F.
N1 - Funding Information:
The author acknowledges the MOE grant ERGS13-024-0057. The author also would like to thank to an anonymous referee whose useful suggestions and comments improve the content of the paper.
Publisher Copyright:
© 2014, Pleiades Publishing, Ltd.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - In the present paper we study recurrence equations over k-ary trees. Namely, each equation is assigned to a vertex of the tree, and they are generated by contractive functions defined on an arbitrary non-Archimedean algebra. The main result of this paper states that the given equations have at most one solution. Moreover, we also provide the existence of unique solution of the equations. We should stress that the non-Archimedeanity of the algebra is essentially used, therefore, the methods applied in the present paper are not valid in the Archimedean setting.
AB - In the present paper we study recurrence equations over k-ary trees. Namely, each equation is assigned to a vertex of the tree, and they are generated by contractive functions defined on an arbitrary non-Archimedean algebra. The main result of this paper states that the given equations have at most one solution. Moreover, we also provide the existence of unique solution of the equations. We should stress that the non-Archimedeanity of the algebra is essentially used, therefore, the methods applied in the present paper are not valid in the Archimedean setting.
KW - non-Archimedean algebra
KW - recurrence equation
KW - tree
KW - unique solution
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U2 - 10.1134/S2070046614040062
DO - 10.1134/S2070046614040062
M3 - Article
AN - SCOPUS:84944181000
SN - 2070-0466
VL - 6
SP - 310
EP - 317
JO - P-Adic Numbers, Ultrametric Analysis, and Applications
JF - P-Adic Numbers, Ultrametric Analysis, and Applications
IS - 4
ER -