Approximation in Lebesgue Space with Variable Exponent by Rational Functions on Carleson Curves
Abstract
In this work, we have proved that any function in the Lebesgue space with variable exponent defined on a rectifiable Jordan curve can be expressed in Faber Laurent series. Then, using this series, the approximation properties in the space , where is variable function satisfying certain conditions, by the partial sums of Faber Laurent series on a large class of curves called Carleson curves are investigated. Moreover, we have estimated the truncation error using the modulus of continuity in the space .
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