Sentence examples for mapping principle guarantees from inspiring English sources

Banach's Contraction Mapping Principle guarantees that has a unique fixed point, say, that is,.

Banach Contraction Mapping Principle guarantees that has a unique fixed point in.

Banach's contraction mapping principle guarantees that has a unique fixed point in.

Banach's contraction mapping principle guarantees that has a unique fixed point in ; that is, (1.22).

Banach's contraction mapping principle guarantees that T t has a unique fixed point.

Then, Banach's contraction mapping principle guarantees that P F (γ f +I - A) has a unique fixed point, say q ∈ H.

Therefore by the Banach Contraction Mapping Principle guarantee that has a unique fixed point, say.

(Banach contraction mapping principle [6]).

Banach contraction principle guarantees that every contractive mapping defined on complete metric spaces has a unique fixed point.

Banach contraction principle guarantees that every contractive mapping defined on complete metric spaces has a unique fixed point. is said to be a weak contraction if (1.2).

Theorem 3.5 ii) allows directly extending Theorem 3.1 as follows by removing the requirement of the set of fixed points to be nonempty with a unique element since this is guaranteed by the Banach contractive mapping principle.