# If f is a function from R to R, and there exists a real number aE(0,1) such that |f'(x)|≤a for all xER , show that the equation x = f(x) has a solution.

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If f is a function from R to R, and there exists a real number aE(0,1) such that |f'(x)|≤a for all xER , show that the equation x = f(x) has a solution.

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6. If f is a function from R to R, and there exists a real number such that for all , show that the equation x = f(x) has a solution.

Proof. Consider a sequence defined by

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