Sentence examples for applying contraction from inspiring English sources

By applying contraction mapping principles and (A3) we obtain the conclusion of the theorem.

In this section, we prove the local existence and uniqueness results to problem (1) by applying contraction mapping theorem, and then we show the global existence using some suitable estimates.

The computational time is approximately consumed as 50% on DEM calculations, 20% on electrical wave propagation, 20% applying contraction to each cell, and 10% solving the single-cell equations.

By applying the contraction principle, we obtain that A is a Picard operator.

Finally we consider the existence of a unique solution for problem (1.1) by applying the contraction mapping principle.

Some sufficient criteria for the existence of solutions are obtained by applying the contraction mapping principle and the fixed point theorem.

By applying the contraction mapping fixed point theorem and exponential dichotomy, we establish sufficient conditions for the existence of a unique almost periodic positive solution.

By applying the contraction mapping principle and the other fixed point theorem, the author obtains the existence and uniqueness of solutions.

By applying the contraction mapping principle and the other fixed point theorem, we obtain the existence and uniqueness of solutions for boundary value problems (simply denoted by BVP).

The problem of contact points between particles, which is inherent to finite-volume numerical methods, is solved by applying a contraction of 2% on all the particles of the bed.

In this paper, we aim to establish sufficient conditions that guarantee the existence of a unique almost periodic positive solution of model (1.2) on time scales by applying the contraction mapping fixed point theorem and exponential dichotomy.