Jñānābha‎, Vol. 48 (1) (2018), 1-16

A NECESSARY AND SUFFICIENT CONDITION FOR THE |Kλ|-SUMMABILITY OF FOURIER SERIES     Pages 1-16

By Prem Chandra 
C-315, Vivekanand Nagar, Ujjain-456010, M.P., India 
Formerly, School of Studies in Mathematics, Vikram University, Ujjain-456010 
E-mail:premchandraujnn@yahoo.in 

Dedicated to the memory of Late Professor S.L. Singh (20.01.1942 to 02.10.2017) (Received : November 19,2017 ; Revised: December 20,2017) 


Abstract 

Recently, in 2015, Sanghamitra, Das and Ray [1] obtained a sufficient condition to ensure |Kλ |-summability of Fourier series. In this paper, we obtain an other condition, imposed upon the generating function of Fourier series, which is best possible in certain sense. 

Keywords and phrases. Absolute summability of Fourier series, Absolute summability by Karamata method. 
2010 Mathematics Subject Classification. 42A28, 40G99