clm55

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15 years, 325 days

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So here's my problem: Find a continuous solution to the integral equation: f(x) = (1/2)*[integral_[0,1](x*y/(y+1))*f(y)dy + x^3] by finding a fixed point of the fucntion psi:(C([0,1]),d_inf) --> (C[0,1]),d_inf) psi(f(x)) = (1/2)*[integral_[0,1](x*y/(y+1))*f(y)dy + x^3] . Here, C([0,1]) is the set of all continuous functions over [0,1] and d_inf is the supremum metric. I honestly have no idea how to do this. My professor said this... A fixed point for the map psi is a solution of the integral equation.
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