Lebl-Basic-Analysis-I · Problem 7.6.4

Metric Spaces

Mathematics · fixed-point-theorem

Problem

Let

F: \mathbb{R} \to \mathbb{R}

be defined by

F(x) \coloneqq kx + b

where

0 < k < 1

b \in \mathbb{R}

. a) Show that

F

is a contraction. b) Find the fixed point and show directly that it is unique.