Sentence examples for upper fixed point from inspiring English sources

A point (x_{ast}inOmega) is called a fixed point (resp. lower fixed point, resp. upper fixed point) if (x_{ast}=Tx_{ast}) (resp. (x_{ast }leq Tx_{ast}), resp.

Condition (4) from the above theorem is equivalent with (4′):  f has a lower or an upper fixed point in X. f has a lower or an upper fixed point in X.

(5′) f has a lower or an upper fixed point in X. Remark 3.5 For some similar results, see Theorem 4.2 and Theorem 4.7 in [37].

T and S commute, that is, (TSx=STx) for each (xinOmega); T and S have at least one common lower (resp. upper) fixed point (u_{0}inOmega) (resp. (v_{0}inOmega)); T is α-condensing; S is a 1-alpha -contractionn.

The set (UF) f = {x ∈ E : x - f(x) ∈ K} is called upper fixed point set of f, (LF) f = {x ∈ E : f(x -x ∈ K} is called lower fix -xpoint set of f and (F) f = {x ∈ E : f(x) = x} is called the set of all fixed points of f.

In this case, the active phase of the burst again initiates at the saddle-node of fixed points SNf, but these oscillations (which are associated with the complex eigenvalues of the upper fixed point, not the periodic orbits) terminate after the slow passage through the subcritical Hopf bifurcation.

A lower (resp. upper) fixed points are also called a post-fixed points (resp. pre-fixed points); see [16], p.264.

Then, is the lower fixed-point set of, while is the upper fixed-point set of.

Note that in the case (( u_{0},v_{0} ) ) is a common upper coupled fixed point of A and B, (( v_{0},u_{0} ) ) is a common lower coupled fixed point of A and B, and the required conclusions follow from the preceding case.

Due to the saturation of G, at higher levels of XT, degradation dominates again, resulting in a convergence from above to the upper stable fixed point.

By using lower and upper solutions method and fixed point index theory, a global result with respect to parameter is established.