Sentence examples for possible fixed point from inspiring English sources

(3.17) Moreover, for any fixed (bar{u}inmathbb{R}), any possible fixed point (tilde{mathbf{u}}) of (tilde{mathcal{A}}(bar{u},cdot)) satisfies Vert tilde{mathbf{u}} Vert < aN.

We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values.

Let us now investigate the case in which we can first establish a nonempty, compact convex, possible fixed point subset of the set (mathcal{F} E, K; T, S)).

Upon scrutinizing the proof of Theorem 1.2, we then placed a suitable compactness on the possible fixed point set (mathcal{F} E, K; T, S)) and obtained an extension of the preceding theorem.

If we can establish a nonempty, compact, possible fixed point subset of the set (mathcal{F} E, K; T, S)) or even of (mathcal{F} M, K; T, S)) with (Msupset K), then the above (iii) is not needed as indicated in the second point above.

p4.: If we can establish a nonempty, compact, possible fixed point subset of the set (mathcal{F} E, K; T, S)) or even of (mathcal{F} M, K; T, S)) with (Msupset K), then the above (iii) is not needed as indicated in the second point above.

Then there exists a constant such that for all and all possible fixed points of at, one has.

Therefore, due to Corollary 4.2 one finds lim_{m rightarrowinfty} V^{(m)}({mathbf{x}})_{1} = 0. Case 2. If (a=1) and (b neqfrac{1}{2}), then we have two possible fixed points.

As shown later the existence of oblique asymptotes is closely related with the number of possible fixed points and bistability.

The solutions are determined by the roots of a polynomial of second degree allowing for two possible fixed points at most.

One of the main directions in obtaining possible generalizations of fixed point results in metric spaces is introducing new types of spaces.