Sentence examples for by utilizing a fixed-point from inspiring English sources

They proved the existence of positive solutions for boundary value problems by utilizing a fixed-point theorem in cones.

We prove the existence of positive solutions for boundary value problem (1.1 - 1.2 1.1 - 1.2zing a fixed point theorem in cones.

By utilizing a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of enterprise clusters based on ecology theory with time-varying delays and feedback controls.

Firstly, we utilize a fixed point theorem to obtain the existence of solution.

(C) By utilizing a well-known fixed point index theorem in cone, the author got some sufficient conditions of the existence and non-existence of positive periodic solutions of (C).

With the help of (2.4), we can complete the proof by utilizing Banach's fixed-point theorem and an argument used frequently to prove the well-posedness of Cauchy problems for ordinary differential equations.

In this section, we first formulate and prove sufficient conditions for the existence and uniqueness of a mild solution of system (1)–(3) by utilizing the fixed-point theory.

The proof of Lemma 3 follows by utilizing the fixed-point principle of Schauder-Tychonoff.

The emerging implicit equations are solved by using a fixed-point iteration scheme.

In this paper, by utilizing a different technique, we prove some coupled fixed point theorems in a partially ordered Φ-orbitally complete normed linear space.

An example of data segmentation utilizing a fixed tumor boundary mask from the first time point is shown in Fig. 9.