Continuous horizontally rigid functions of two variables are affine
نویسندگان
چکیده
منابع مشابه
Continuous Rigid Functions
A function f : R→ R is vertically [horizontally] rigid for C ⊆ (0,∞) if graph(cf) [graph(f(c ·))] is isometric with graph(f) for every c ∈ C. f is vertically [horizontally] rigid if this applies to C = (0,∞). Balka and Elekes have shown that a continuous function f vertically rigid for an uncountable set C must be of one of the forms f(x) = px+q or f(x) = pe + r, this way confirming Jancović’s ...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2012
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-011-0110-1