5 Assume that f R R is such that f x f y X x y for all x y E

Last updated: 3/20/2023

5 Assume that f R R is such that f x f y X x y for all x y E R and some 0 1 Pick xo E R arbitrarily and construct a sequence xn as follows In 1 f xn for n 0 a Prove that n 1 Xn xn Xn 1 for all n 1 b Prove that n 1 xn x xo for all n 1 c Prove that n is convergent d Let x limxn Prove that f x x