An Estimate of the Rate of Convergence of the Fourier Series in the Generalized Hölder Metric by Delayed Arithmetic Mean
An Estimate of the Rate of Convergence of the Fourier Series in the Generalized Hölder Metric by Delayed Arithmetic Mean
We study the rate of convergence problem of the Fourier series by Delayed Arithmetic Mean in the generalized Hölder metric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>w</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math> space which was earlier introduced by Das, Nath, and Ray and obtain a sharper estimate of Jackson's order.