Sentence examples for be a continuous mappings from inspiring English sources

Let F : X × X → X be a continuous mappings satisfying the mixed monotone property.

Let be a reflexive Banach space with the dual space let be two continuous mappings, and let be a continuous mapping.

Theorem 3.2 Let ρ ∈ ℜ and let F = { T t : t ≥ 0 } be a continuous semigroup of mappings on a subset C of L ρ.

0 < α n + 1 < α n for all n ∈ N ; k n ∈ N for all n ∈ N ; α n / α n + 1 ∉ Q for all n ∈ N ; { α n } converges to 0. Theorem 3.3 Let ρ ∈ ℜ and let F = { T t : t ≥ 0 } be a continuous semigroup of mappings on a subset C of L ρ.

Let { T ( t ) : t ∈ R } be a continuous semigroup of nonexpansive mappings on C. Let { t n } be a sequence in R +.

Let { Q ( q ) : q ∈ R } be a continuous semigroup of nonexpansive mappings on C. Let { q n } be a sequence in R +.

Theorem 3.4 Let ρ ∈ ℜ be (UUC), and let F = { T t : t ≥ 0 } be a continuous semigroup of ρ-nonexpansive mappings on a ρ-closed, ρ-bounded, convex, nonempty subset of L ρ.

Let F = { T t : t ≥ 0 } be a continuous semigroup of ρ-nonexpansive mappings on C. Assume that α > 0 and β > 0 are two real numbers such that α / β ∉ Q. Fix λ, κ ∈ ( 0, 1 ) such that κ + λ < 1. Define a sequence { x n } in C by x 1 ∈ C and x n + 1 = κ T α ( x n ) + λ T β ( x n ) + ( 1 − κ − λ ) x n (4.21).

Since is a continuous, pseudocontractive mappings weakly inward on, then is an accretive operator with the range condition (see [11, 15]).

Assume that lim n → ∞ q n = lim n → ∞ α n q n = 0. Then lim n → ∞ x n = x ¯ for some x ¯ ∈ Ω. Proof For each t ≥ 0, let T ( t ) : C → C be defined by T ( t ) x : = x for each x ∈ C. Clearly, { T ( t ) : t ≥ 0 } is a continuous semigroup of nonexpansive mappings on C. Since C is a compact set, Ω : = ⋂ q ≥ 0 F ( Q ( q ) ) ≠ ∅.

The following properties hold: (i) assume that is a nonempty complete metric space and that is a continuous surjective -times reasonable expansive self-mapping according to Theorem 3.10 so that it has a fixed point in X.