On the necessary conditions for absolute weighted arithmetic mean summability factors

A new note on factored infinite series and trigonometric Fourier series

“…Many works dealing with the absolute summability factors of infinite series and Fourier series have been done (see [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][25][26][27][28][29][30][31][32][33][34][36][37][38][39][40]). Among them, in [12], the following theorem has been proved.…”

Characterization of summability methods with high indices

“…(see [13] Problems on inclusion dealing absolute Cesàro and absolute weighted mean summabilities have been examined by many authors ( [3][4][5][6][7][8][9][10][11][12][13][14]). …”