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- W2004066649 abstract "This paper is concerned with approximation on variable<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mo>·</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>spaces associated with a general exponent function<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>and a general bounded Borel measure<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow></mml:math>on an open subset<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi mathvariant=normal>Ω</mml:mi></mml:mrow></mml:math>of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>. We mainly consider approximation by Bernstein type linear operators. Under an assumption of log-Hölder continuity of the exponent function<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>, we verify a conjecture raised previously about the uniform boundedness of Bernstein-Durrmeyer and Bernstein-Kantorovich operators on the<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mo>·</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>space. Quantitative estimates for the approximation are provided for high orders of approximation by linear combinations of such positive linear operators. Motivating connections to classification and quantile regression problems in learning theory are also described." @default.
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- W2004066649 title "Analysis of Approximation by Linear Operators on Variable<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msubsup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mo>·</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>Spaces and Applications in Learning Theory" @default.
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