Absolute Nevanlinna Summability and Fourier Series

We adopt here an extended version of the absolute Nevanlinna summability and apply it to study Fourier series of functions of bounded variations. The absolute Riesz summability R, n, , 0, which is equivalent to the absolute Ces`aro summability C, , is obtainable from the Nevanlinna summability. As such from the theorems proved here we deduce some results on the absolute Ces`aro summability of Fourier series. Some of these results are new while some others improve upon known theorems