Sentence examples for application of contraction from inspiring English sources

Application of contraction theory provides an alternative way for stability analysis of nonlinear systems.

For applications of contraction principles to variational relations, the reader is referred to [4].

It is necessary to mention that the applications of contraction, generalized contraction principle for self-mappings, and the applications of nonlinear contractions are well known.

A standard application of the contraction mapping theorem leads to the following existence result.

Some of the articles present the application of F-contractions to integral and functional equations [3], iterated function systems [4], Volterra-type integral equations [5] and integral inequalities [6].

Now, a natural question is what further conditions are to be imposed on T or α to guarantee the existence of a fixed point for T? For some partial answers to this question and application of quasi-contraction maps to variational inequalities, see [4] and the references therein.

Impulsive uncertain BAM neural networks modeling brings about some mathematical difficulties to the applications of the contraction mapping theorem.

After this a great deal of effort has gone into the theory and application of the Banach contraction theorem.

Then the system (23) has a unique solution, which is of the form ( f 0, f 0, f 0 ), where f 0 ∈ L 1 ( I ) is the only solution of the equation f 0 ( x ) = A + ∫ [ a, x ] G ( f 0 ( t ), f 0 ( t ), f 0 ( t ) ) d t for all  x ∈ I. (this exists as a simple application of the Banach contraction principle).

Topical application of GSPE accelerated wound contraction and closure.

The application of Hs.Cr to spontaneous contractions of isolated rabbit jejunum preparations (Fig.  1b) provoked a concentration-dependent (0.01-3.0 mg/ml) relaxant effect after addition in a cumulative manner; the EC50 value was 0.381 mg/ml (95 % CI: 0.043-1.478 mg/ml; n = 5) (Fig.  2a).