Sentence examples for mapping principle of from inspiring English sources

The classical contraction mapping principle of Banach is one of the most powerful theorems in fixed point theory because of its simplicity and usefulness.

It is well known that the contraction mapping principle of Banach [1] was the starting point of great discoveries and advances in mathematics, in particular in nonlinear analysis.

Therefore, Corollary 3.4 is a real proper extension of the Banach contraction mapping principle of Banach [29] because the continuity of the mapping T is not required.

The classical contraction mapping principle of Banach states that if ( X, d ) is a complete metric space and f : X → X is a contraction mapping, i.e., d ( f ( x ), f ( y ) ) ≤ α d ( x, y ) for all x, y ∈ X, where α ∈ [ 0, 1 ), then f has a unique fixed point. Banach fixed point theorem plays an important role in several branches of mathematics.

The classical contraction mapping principle of Banach states that if ((X,d)) is a complete metric space and (f:X to X) such that (d(f(x),f y)) lealpha d x,y)) for all (x,y in X), where (alpha in[0,1)), then f has a unique fixed point.

Although Branciari [3] correctly stated the analog of Banach contraction mapping principle in the setting of Branciari metric space, proofs has gaps which was removed by a number of authors; see e.g. [5, 12, 19, 31].

The authors discussed the topological properties of this space and proved the analog of the Banach contraction mapping principle in the context of G-metric spaces (see e.g. [8 15]).

We conclude the results from the characterization of the Banach contraction mapping principle in the context of b-metric space (see, e.g., [[14], Theorem 2]).

In 2006, Mustafa and Sims [49] introduced the notion of a G-metric spaces as a generalization of the concept of a metric space and proved the analog of the Banach contraction mapping principle in the context of G-metric spaces.

Remark 3.1 Note that the Corollary 3.3 is a proper extension of the contraction mapping principle [13] because the continuity of the mapping T is not required.

In 2003, Ran and Reurings characterized the Banach contraction mapping principle in the context of partially ordered metric space.