Existence and Uniqueness of the Solution to Cauchy Problem

This presentation covers some key concepts in metric spaces, including Banach's fixed-point theorem, notions of convergence, normed spaces, spaces of continuous functions, and the Picard–Lindelöf theorem.

Overview

• Metric spaces
• Banach's fixed-point Theorem
  • Proof for uniqueness of a fixed-point
  • Proof for existence of a fixed-point
• Pointwise and Uniform convergence
• Normed spaces
• Space of continuous functions
• Picard–Lindelöf Theorem
• References