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([6]) Let y : I → ℝ be a continuously differentiable function satisfying the differential inequality y ′ ( t ) + g ( t ) y ( t ) + h ( t ) ≤ φ ( t ). for all t ∈ I, where g, h : I → ℝ are continuous functions and φ : I → [0, ∞) is a function. Assume that.
Let (f:mathbb{R}^{m times n} to mathbb{R}) be a continuously differentiable function with Lipschitz continuous gradient and the Lipschitz constant (L ( f )).
be a continuously differentiable function.
Let be a continuously differentiable vector-function.
Let (x t)) be a continuously differentiable T-periodic function.
Let (u(t)) be a continuously differentiable T-periodic function.
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The result is a continuously differentiable analytic expression that can be used to determine the error source term.
f is a continuously differentiable function.
It is obvious that F is a continuously differentiable mapping.
If is a continuously differentiable and monotone function in and in, then the objective of (26) is a continuously differentiable and monotone function in.
where,, and are as in Section 4.1, is a continuously differentiable matrix.
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