Věty o pevných bodech

Abstract

In this bachelor thesis we first take a look at fixed points and then fixed points of function f:ℝ → ℝ. After that we define metric space and concepts needed to formulation and proof of Banach fixed-point theorem. Then we show some applications of Banach fixed-point theorem (numerical calculation of the square root, solving systems of equations, implicit function theorem, theorem on the existence and uniqueness of solutions of the Cauchy problem), where Banach fixed-point theorem will give us method to find solution which we will show in the examples.