- #1

datenshinoai

- 9

- 0

## Homework Statement

Let K: [0,1] x [0,1] -> R be a continuous function such that K(x,y) > 0 and the integral K(x,y) dy <= C < 1 (from 0 to 1) for all x within [0,1].

Let g:[0,1] -> R be any continuous Function. Show that there is a unique continuous function f:[0,1] -> R such that f(x)= g(x) + integral K(x,y) dy

## The Attempt at a Solution

I know that we are given 2 functions and that we need to input those into the formula. We want to see the output is closer than the input by a factor of k, but I'm not sure what it is that I should be doing.

To show uniqueness, I say to let g(f(x)) = h(x). Which means we are sending [0,1] -> R to [0,1] -> R, but I don't think that's right...

Thanks in advance!