Sentence examples for mapping with constants from inspiring English sources

Let be   -Lipschitz continuous mapping with constants,,,, respectively.

Let f : K → R be a real valued convex function and assume that ∇f is 1 L -inverse strongly monotone mapping with L ≥ 0. Let A : K → H be a k-Lipschitz continuous and η-strongly monotone mapping with constants k, η > 0 and 0 < μ < 2 η k 2, τ = μ ( η − μ k 2 2 ).

A mapping A : X × X → X is said to be a restricted-accretive mapping with constants ( α 1, α 2 ), if A is a comparison, and there exist two constants 0 < β 1, β 2 ≤ 1 such that for arbitrary x, y ∈ X, ( A ( x, ⋅ ) + I ( x ) ) ⊕ ( A ( y, ⋅ ) + I ( y ) ) ≤ β 1 ( A ( x, ⋅ ) ⊕ A ( y, ⋅ ) ) + β 2 ( x ⊕ y ).

Let U : Ω ↦ H be a γ-Lipschitzian mapping with a constant γ ≥ 0 and let F : Ω ↦ H be a k-Lipschitzian and η-strongly monotone mapping with constants k, η > 0, then for 0 ≤ ρ γ < μ η, 〈 x − y, ( μ F − ρ U ) x − ( μ F − ρ U ) y 〉 ≥ ∥ x − y ∥ 2, ∀ x, y ∈ Ω.

Then (T_{1}), (T_{2}) and (T_{3}) are nonexpansive mappings, and f is a contraction mapping with constant (frac{2}{7}).

Let be a bifunction from into satisfying (a1)–(an), an inverse-strongly monotone mapping with constant, an inverse-strongly monotone mapping with constant, a contraction mapping with constant.

Put, where is a strictly pseudo-contractive mapping with constant.

Since is a Lipschitz mapping with constant, we have (2.9).

Let be a contraction mapping with Lipschitz constant and let be an inverse-strongly monotone mapping with constant.

Let be a nonempty closed convex bounded subset of a real Hilbert space, a multivalued -Lipschitz continuous mapping with constant, a contraction mapping with constant.

Let be a nonempty closed convex bounded subset of a real Hilbert space, a Lipschitz continuous mapping with constant, a contraction mapping with constant.