Approximation Operators for Vector-Valued Functions
Let (E, < ·, · >) be a Euclidean space with the norm denoted by ‖ · ‖. Let I = [a, b], a < b be a real interval. Let C(I, E) be the space of continuous functions, endowed with the sup-norm denoted by ‖ · ‖ I and denote by C k (I, E), k ≥ 1, the subspace of functions having a continuous derivative of order k on I. If φ : I → ℝ and w ∈ E we denote by φw, the function (φw)(x) = φ(x)w.
KeywordsBanach Space Approximation Operator Convex Operator Linear Positive Operator Real Argument
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