Linked from

The 24 pages that link to Banach fixed-point theorem, each with the reason it gives.

• Brouwer fixed-point theoremCompared with: Unlike Brouwer's existence-only result, it requires contraction and provides uniqueness and an iterative method.

• Hahn–Banach theoremCompared with: It also bears Banach's name but concerns iterative existence, not linear-functional extension.

• Inverse function theoremCompared with: It can prove local solvability by iteration rather than by the inverse theorem's differential criterion.

• Lax–Milgram theoremCompared with: It is another route to well-posedness, but requires a contraction rather than coercivity.

• Schauder fixed-point theoremCompared with: Unlike Schauder’s theorem, it requires contraction but gives uniqueness and iterative convergence.

• Lefschetz fixed-point theoremCompared with: It uses metric contraction rather than homology to guarantee a unique fixed point.

• Kleene's recursion theoremCompared with: Unlike Banach's theorem, this result concerns computable program behavior rather than metric convergence.

• Kirszbraun theoremCompared with: It concerns maps that shrink distances, rather than extending maps while preserving distances.

• Kleene fixed-point theoremCompared with: It obtains fixed points through metric contraction, rather than order and directed continuity.

• Knaster–Tarski theoremCompared with: It uses metric contraction rather than order preservation and gives uniqueness rather than a lattice of solutions.

• Caristi fixed-point theoremCompared with: Banach requires uniform distance contraction; Caristi instead uses a decreasing potential.

• Fredholm's theoremCompared with: It proves uniqueness by contraction, not by the Fredholm alternative's range conditions.

• Lions–Lax–Milgram theoremCompared with: It offers a general alternative route to existence and uniqueness through contraction.