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In this paper, we show the uniqueness of polynomial of best approximation of a function f ∈ E = C([a, b]) by a polynomial of degree ≤ n and to characterize it. Then introduce the algorithm of Remez and prove its convergence. Illustrations and numerical simulations are given to prove the efficiency of our work.
In this paper we consider the following Timoshenko system ϕ tt − (ϕ x + ψ) x = 0, (0, 1) × (0, +∞) ψ tt − ψ xx + t 0 g(t − τ)(a(x)ψ x (τ)) x dτ + ϕ x + ψ + b(x)h(ψ t) = 0, (0, 1) × (0, ∞) with Dirichlet boundary conditions where a, b, g, and h are specific functions. We establish an exponential and polynomial decay results. This result improves and… (More)
In this paper, we consider vibrating system of Timoshenko type in one-dimensional bounded domain with complementary past history and frictional damping controls acting only in the equation for the rotation angle. We show that the dissipation given by this complementary controls is strong enough to guarantee the stability of the system in case of the same… (More)