Sentence examples for be a nonempty subadmissible from inspiring English sources

Let be a nonempty subadmissible subset of a metric space.

Let ( M, d ) be a metric space, X be a nonempty subadmissible subset of M and F ∈ KKM ( X, X ).

Theorem 3.8 Let ( M, δ ) be a circular metric space, X be a nonempty subadmissible subset of M and F ∈ KKM ( X, X ).

Theorem 3.13 Let M ω be a modular metric space, X be a nonempty subadmissible subset of M and F ∈ KKM ( X, X ).

Lemma 3.11 Let ( M, δ ) be a circular metric space, Y be a topological space and X be a nonempty subadmissible subset of M. Suppose that f : Y → X is continuous.

Corollary 3.12 Let ( M, δ ) be a circular metric space, Y be a topological space and X be a nonempty subadmissible subset of M. Suppose that f : X → X is continuous and f ( A ) ¯ is bounded and compact for all nonempty bounded subset A of X.

Let be an nonempty subadmissible subset of a metric space, and let a topological space.

Then whenever, and is a nonempty subadmissible subset of.

Since and is a nonempty subadmissible subset of, by Lemma 2.6,.

Assume that X is a nonempty subadmissible subset of a circular metric space ( M, δ ), and let φ : X × X → R and H X ⊸ ⊸ X be given.

Let be a nonempty bounded subadmissible subset of a metric space.