Sentence examples for maps considered in from inspiring English sources

In this section we will study the sum of two mappings belonging to the different classes of contractive maps considered in Theorem 1.2.

As in the case of 1-equivariant wave maps considered in [9], both problems admit a family of stationary solutions indexed by a parameter that determines how far the image of the map wraps around the target manifold.

The following condition provides the uniqueness of fixed points of the maps considered in Theorem 2.3 and Theorem 2.4.

Let us show that the convexity of a metric space is essential for equivalence of the properties of q-Lipschitzness in the metrics dist, ρ cl, ρ S. Note that the maps considered in Examples 3 and 4 are contracting (with a constant q = 1 / 3 ) in the metrics ρ S and ρ cl.

(2) Theorem 3.2 improves and generalizes the results in Zhao and Chang [26] in a number of ways: The class of maps considered in Zhao and Chang [26] is extended from the class of uniformly quasi-ϕ-asymptotically nonexpansive single-valued nonself maps to the slightly more general class of countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps.

The biomass maps considered in this study were obtained by combining biomass reference values with spatial datasets.

There is a limit to the asymmetry-induced stability gain, since the instability occurs over a broader region in the stability map considered in the present investigation.

If ψ is of the form of ψ = kε (k ∈ (0, 1)), one obtains the contractive mapping considered in [3].

Continuity of the map considered in (16) and compactness of the closed balls B ̄ ( Θ 0, ε ), B ̄ ( Z 0, ε 0 ) ensures |M1|<∞.

Throughout the paper, (F(T)) denotes the set of fixed points of the mapping T. The contraction mappings considered in this paper are constructed via auxiliary functions defined below.

The estimated flow and growth are shown in (B1) and (C1), respectively, for the case in which 4 maps are considered, in (B2) and (C2) in the case in which 6 maps are used, and in (B3) and (C3) for the case in which 16 maps are processed.