Does this function have to be constant?
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Suppose that a continuous function $f : [0,1] to mathbb{R}_+$ satisfies the following property for all $x in [0,1]$ : $$ f(x) = frac{3}{2} fleft(frac{3}{4} xright) - frac{1}{2} fleft(frac{1}{2} xright). $$ For example: this is clearly satisfied when $f(x) =c = frac{3}{2}c-frac{1}{2}c$ . Are there other functions that satisfy this property?
functional-analysis functions
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asked Jan 2 at 18:15
TomH TomH
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