Sentence examples similar to a closed setting from inspiring English sources

Corollary 3.1 Let ( X, f ) be a classical dynamical system and A be a nonempty closed set of X.

Proposition 3.1 Let ( X, f 1, ∞ ) be a non-autonomous discrete system and A be a nonempty closed set of X.

It is well known that if X is a reflexive Banach space and (Gsubset X ) is a convex closed set, then G is a proximal set, while if X is a strictly convex Banach space and G is a convex closed set, then G is a semi-Chebyshev set (see [8]).

Let D be a convex, closed set in a Banach space E with (0in D).

Proof According to Corollary 9.1 we have to prove that U ¯ ( a, r ) is a sequentially closed set.

Let us remember that the metric projection on a convex closed set is a firmly nonexpansive mapping (see [19]) so we claim that have the following proposition.

A nonempty closed set is called a cone, if it satisfies the following two conditions: (i) for all and all ; (ii) implies.

In this paper, informed by the characteristics of the nonlinear term we construct a new cone, and through this cone create a convex closed set.

Hence is a nonempty closed set.

Let (mathbb{T}subsetmathbb{R}) be a nonempty closed set.

where is a nonempty closed set since is compact.