Approximation in Lebesgue Space with Variable Exponent by Rational Functions on Carleson Curves - علي محمد; خليفة حسن; كنج بشار (Latakia University Journal -Basic Sciences Series, 2021)
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 .