Some Aspects of Theory and Applications of Summability and its Developments
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Abstract
If
newlinef
newlineis a
newline2and#61552; and#61485; Periodic function of the class
newlineLipand#61480;and#61537;,rand#61481;
newline, then
newlinedegree of approximation by the product
newlineand#61480; and#61481;and#61480; and#61481; E q N pn
newline, ,
newlinesummability
newlinemeans on its Fourier series is given by
newlineand#61480; and#61481;
newline,0 1, 1
newline1
newline1
newline1
newlineand#61500; and#61500; and#61619;
newlineand#61687;
newlineand#61687;
newlineand#61687;
newlineand#61688;
newlineand#61686;
newlineand#61671;
newlineand#61671;
newlineand#61671;
newlineand#61672;
newlineand#61670;
newlineand#61483;
newlineand#61485; and#61501;
newlineand#61483;
newlineand#61605;
newliner
newlinen
newlinef O
newliner
newlineand#61556; n and#61537;
newlineand#61537;
newline,
newlinewhere
newlinen
newlineand#61556;
newlineis the
newlineand#61480;E,rand#61481;and#61480;N, p,qand#61481;
newlinemean of the series.
newline