Sentence examples for mapping principle is from inspiring English sources

The Banach contraction mapping principle is a classical and powerful tool in nonlinear analysis.

In the Hilbert space setting, the Banach contraction mapping principle is as follows.

The Banach-contraction mapping principle is one of the pivotal results of analysis.

It is well known that the Banach contraction mapping principle is one of the pivotal results of analysis.

The Banach contraction mapping principle is considered to be the core of many extended fixed point theorems.

Here, 0 is the fixed point of T. Notice also that the Banach contraction mapping principle is not applicable.

It is obvious that the conditions for contraction mapping principle are too strong.

One of the celebrated generalizations of the Banach contraction (mapping) principle was given by Geraghty [1].

In particular, one of the interesting generalizations of the Banach contraction mapping principle was given by Geraghty [1].

Another interesting generalization of the Banach contraction mapping principle was given by Kirk et al. [13] via a cyclic mapping (see, e.g., [14 16]).

The following generalization of the Banach contraction mapping principle was proved by Rakotch [1]: if ϕ is monotone and continuous, then any ϕ-contraction is a Picard operator.