@article{article_506424, title={Summability of Fourier Series and its Derived Series by Matrix Means}, journal={Journal of New Theory}, pages={54–63}, year={2019}, author={Karazon, Abdelhadi Mohammad and Amer, Mohammad Mahmoud}, keywords={Summability,matrix summability,Fourier series,derived Fourier series}, abstract={<p class="MsoNormal" style="text-align:justify"> <span lang="EN-US" style="font-size:10.0pt;mso-ansi-language:EN-US;mso-bidi-language:AR-SY">This Paper introduces the concept of matrix operators and establishes two new theorems on matrix summability of Fourier series and its derived series. the results obtained in the paper further extend several known results on linear operators. Various types of criteria, under varying conditions, for the matrix summability of the Fourier series, In this paper quite a different and general type of criterion for summability of the Fourier Series has been obtained, in the theorem function </span> <!--[if supportFields]> <span lang=EN-US style=’font-size:10.0pt;mso-ansi-language:EN-US;mso-bidi-language:AR-SY’> <span style=’mso-element:field-begin’> </span> <span style=’mso-spacerun:yes’>  </span>QUOTE </span> <span lang=EN-US style=’position:relative;top:2.5pt;mso-text-raise:-2.5pt; mso-ansi-language:EN-US’> <![if gte vml 1]> <v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype> <v:shape id="_x0000_i1025" type="#_x0000_t75" style=’width:3pt; height:12pt’ equationxml="<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
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