Sentence examples for a proper subclass of from inspiring English sources

Obviously, the nonexpansive mapping class is a proper subclass of the strict pseudo-contraction class and the Lipschitzian operator class is a proper subclass of the boundedly Lipschitzian operator class, respectively.

We showed that the s-recursively contractible complexes are a proper subclass of the retractable complexes: Theorem 5.1.

That is, the class of strongly accretive operators is a proper subclass of the class of ϕ-strongly accretive operators.

From Example 3.1 we see that (boldsymbol{Phi}_{mathbf{w}^) is a proper subclass of (boldsymbol{Phi}_{mathbf{w}}).

Furthermore, the class of asymptotically k-strictly pseudocontractive mappings is a proper subclass of the class of asymptotically pseudocontractive maps.

To see that the class of convex functions is a proper subclass of Jensen-convex functions, see [2, page 96].

Let us call such a class a proper subclass of an ontological category, a natural class that is neither the class of all things nor one of the ontological categories an 'ontological sub-category'.

In recent works several authors claimed to introduce some weaker noncommuting notions and showed that their introduced noncommuting conditions contain weak compatibility as a proper subclass.

Indeed, the classes of proximal contractions of the first kind and the second kind are proper subclasses of these classes.

We notice that the set (class) of all well-known b-metric spaces ((bge1)) can be a proper subset (subclass) of the set (class) all transversal r-max edges space for (rge1).

We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's classification conjecture: two C∗-algebraic (Z-stability and approximate divisibility), one K-theoretic (strict comparison of positive elements), and three topological (finite decomposition rank, slow dimension growth, and bounded dimension growth).