Sentence examples for mapping principle to from inspiring English sources

In 1965, Prešić [36] extended the Banach contraction mapping principle to mappings defined on product spaces and proved the following theorem.

In 1965, Prešić [4, 5] extended the Banach contraction mapping principle to mappings defined on product spaces and proved the following theorem.

Then we use the Banach contraction mapping principle to deduce (2.1).

Nadler [1] generalized the Banach contraction mapping principle to set-valued functions and proved the following fixed point theorem.

Now we use the Banach contraction mapping principle to prove that the boundary value problem (1.1 - 1.2 1.1 - 1.2ique solution on ([0,1]).

In this section, we use the Banach contraction mapping principle to prove the existence and uniqueness of the solution of problem (1.1).

Banach contraction mapping principle [1] is considered to be the initial and fundamental result in this direction.

Zhang et al. [11] introduced a multi-label classification method based on kNN which uses a Maximum a Posteriori (MAP) principle to predict the class of an new element.

So according to the uniform contraction mapping principle, we can obtain the result of the theorem.

(Banach contraction mapping principle [6]).

There are a lot of generalizations of the Banach contraction mapping principle in the literature.