Sentence examples for multiple fixed points from inspiring English sources

We establish the condition for existence of multiple fixed points and examine the stability of the fixed points in each case.

The same results on multiple fixed points can be derived from other theorems.

Remark 3.5 We stress that the above theorems can be combined to prove the existence of multiple fixed points.

In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized.

Furthermore, particular care has to be taken in systems possessing multiple fixed points of the macroscopic equation, and we refer to [5] for a discussion of this aspect in the neural field setting.

By using a multiple fixed point theorem (Avery-Peterson fixed point theorem) for cones, some criteria are established for the existence of three positive periodic solutions for a class of higher-dimensional functional differential equations with impulses on time scales of the following form:,,, where is a nonsingular matrix with continuous real-valued functions as its elements.

The main purpose of this paper is to establish some sufficient conditions for the existence of at least three positive periodic solutions in shifts δ ± of system (1.1) using a multiple fixed point theorem (Avery-Peterson fixed point theorem) in cones.

Our results are obtained via some new multiple fixed point theorems.

By using the well-known Leggett-Williams multiple fixed point theorem, the authors obtained the existence of multiple positive periodic solutions of problem (1.1).

Much of this interest has been spurred on by the applicability of the topological method such as the upper and lower solutions technique [2], a number of new fixed point theorems and multiple fixed point theorems [3 7] as applied to certain discrete boundary value problems.

In short, considering a life-size moving object found in the construction field (like the rigging system used in the case study of the present research), the inclusion of multiple fixed control points in each photo frame is infeasible.