On $ (J, p_n) $ summability of fourier series

Authors

  • Satish Chandra

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.378

Abstract

In this paper we prove the following two theorems for $ | J, p_n | $ summability of fourier series, which generalizes many previous result:

Theorem 1.  If

$$ \Phi (t) = \int_t^{\pi} \frac{\phi (u)}{u} du = o \{ p (1- \frac{1}{t} ) \} ~~~~ (t \to 0) $$

then the Fourier series for $ t = x $ is summable $ (J, p_n) $ to sum $ s $.

Theorem 2.  If

$$ G(t) = \int_t^{\pi} \frac{g(u)}{u} du = o \{ p(1-\frac{1}{t}) \} ~~~~ (t \to 0) $$

then the differentiated Fourier series is summable $ (J, p_n) $ to the value $ C $.

Author Biography

Satish Chandra

Department of Mathematics, S. M. Post-graduate College, Chandausi-202412 (U.P.), India.

Published

2001-09-30

How to Cite

Chandra, S. (2001). On $ (J, p_n) $ summability of fourier series. Tamkang Journal of Mathematics, 32(3), 225–230. https://doi.org/10.5556/j.tkjm.32.2001.378

Issue

Section

Papers