@article{Chandra_2001, title={On $ (J, p_n) $ summability of fourier series}, volume={32}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/378}, DOI={10.5556/j.tkjm.32.2001.378}, abstractNote={<p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">In this paper we prove the following two theorems for $ | J, p_n | $ summability of fourier series, which generalizes many previous result: </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">Theorem 1. <span style="mso-spacerun: yes;"> </span>If </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">$$ \Phi (t) = \int_t^{\pi} \frac{\phi (u)}{u} du = o \{ p (1- \frac{1}{t} ) \} ~~~~ (t \to 0) $$ </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">then the Fourier series for $ t = x $ is summable $ (J, p_n) $ to sum $ s $. </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">Theorem 2.<span style="mso-spacerun: yes;">  </span>If </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">$$ G(t) = \int_t^{\pi} \frac{g(u)}{u} du = o \{ p(1-\frac{1}{t}) \} ~~~~ (t \to 0) $$ </span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: #000000; font-family: Verdana;">then the differentiated Fourier series is summable $ (J, p_n) $ to the value $ C $.</span></p>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Chandra, Satish}, year={2001}, month={Sep.}, pages={225–230} }