Sentence examples for an example of a map from inspiring English sources

Next, we give an example of a map which lacks assumption (2) and has no fixed point.

In [1] the authors gave an example of a map which is contraction for but not for the euclidian distance.

Further, an example of a map which is an F-contraction while it is not a Banach contraction was given.

We give an example of a simplicial complex in Figure 3(a) and an example of a map of simplicial complexes in Figure 3(b).

The search for routes yielded 513 unique random usernames of runners (see Figure 3 for an example of a map showing the result of the search for routes of one runner, with individual runs depicted with different colours).  .

With respect to the metric dist, they are only Lipschitz with a constant q > 1. Give an example of a map that is contracting in the metric ρ cl and not Lipschitz in the metric dist.

Listing 3 presents an example of a map-reduce query mrq, which counts the emails sent to addresses which have received at least one email.

Next we give an example of a mapping which is not a pointwise contraction, but fulfills (3.7).

We also provide an example of a mapping for which the conclusion of Banach contraction principle fails but admits one of our fixed point results.

Khamsi et al. demonstrated in [2] that a mapping T is norm-nonexpansive in a modular function space L ρ if and only if ρ ( λ ( T ( f ) − T ( g ) ) ) ≤ ρ ( λ ( f − g ) ) for any  λ ≥ 0. They also gave an example of a mapping which is ρ-nonexpansive, but it is not norm-nonexpansive.

We give an example of a mapping T : C → C which satisfies all the assumptions of T in Theorem 3.4, i.e., T : C → C is a uniformly continuous mapping with F ( T ) ≠ ∅ which is TAN on C, not Lipschitzian and hence not asymptotically nonexpansive.