Sentence examples for be a jointly continuous from inspiring English sources

Theorem 3.2 Let f : [ 0, 1 ] × R → R be a jointly continuous function.

Let (f: [0,1]times{mathbb{R}} to{mathbb{R}}) be a jointly continuous function.

Let (f : [0,1]timesmathbb{R} tomathbb {R}) be a jointly continuous function satisfying the assumption (A1).

Theorem 3.1 Let f : [ 0, 1 ] × R → R be a jointly continuous function satisfying the Lipschitz condition.

Let (f: [0,T]times mathbb{R} to mathbb{R}) be a jointly continuous function and (I_{k}, J_{k}: mathbb{R} to mathbb{R}) be continuous functions.

Theorem 3.2 Let f : I q × ℝ → ℝ be a jointly continuous function satisfying the Lipschitz condition f ( t, u ) - f ( t, v ) ≤ L u - v, ∀ t ∈ I q, u, v ∈ ℝ, where L is a Lipschitz constant.

Suppose that (f: [0,1]timesmathbb{R} tomathbb{R}) is a jointly continuous function.

Assume that (f : [0,1]timesmathbb{R} to mathbb{R}) is a jointly continuous function satisfying (H1).

Assume that is a jointly continuous function and satisfies the assumption Then the boundary value problem (1.1) has a unique solution provided, where is given in the assumption.

Assume that (f : [0,1]times{mathbb{R}} to {mathbb{R}}) is a jointly continuous function and satisfies the assumption (A1):  (|f t,x -f t,x -f t L |x-y|),y(forall t in [0,1]), (L>0), (x, yin{mathbb{R}}), with (L < 1/Lambda), where Λ is given by (3.6).

If f : I × C σ → E d is a jointly continuous function and x ∈ C ( J, E d ), then the mapping t → f ( t, x t ) is bounded on each compact interval I. Also, the function t → f ( t, 0 ˆ ) is bounded on I.