The Nörlund summability
was first applied to the theory of Fourier series by E. Hille and J. D. Tamarkin. Many
other mathematicians have since worked in this field. Recently T. Singh has proved a
nice theorem conceming the Nörlund summability of Fourier series. In Part I, we
shall give a generalization.
Absolute Nörlund summability was defined by L. McFadden and he
proved a theorem concerning the absolute Nörlund summability of the
Fourier series of functions of the Lipschitz class which was generalized by
S. N. Lal. We shall give another generalization of McFadden’s theorem in
Part II.