Shape Preserving Widths of Weighted Sobolev-type Classes of Positive, Monotone and Convex Functions on a Finite Interval
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چکیده
Let X be a real linear space of vectors x with a norm ‖x‖X , W ⊂ X, W 6= ∅ and V ⊂ X, V 6= ∅. Let L be a subspace in X of dimension dim L ≤ n, n ≥ 0 and M = M(z) := z + L be a shift of the subspace L by an arbitrary vector z ∈ X. If M ∩ V 6= ∅, then we denote by E(x, M ∩ V )X := inf y∈Mn∩V ‖x− y‖X , the best approximation of the vector x ∈ X by M ∩ V , and by E(W,M ∩ V )X := sup x∈W E(x,M ∩ V )X ,
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SHAPE PRESERVING WIDTHS OF SOBOLEV-TYPE CLASSES OF s-MONOTONE FUNCTIONS ON A FINITE INTERVAL
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