© Hindawi Publishing Corp. ON ALMOST (N,p,q) SUMMABILITY OF CONJUGATE FOURIER SERIES

Abstract. A new theorem on almost generalized Nörlund summability of conjugate series of Fourier series has been established under a very general condition. 2000 Mathematics Subject Classification. Primary 42B05, 42B08. 1. Introduction. Lorentz [3], for the first time in 1948, defined almost convergence of a bounded sequence. It is easy to see that a convergent sequence is almost con-vergent [4]. The idea of almost convergence led to the formulation of almost gener-alized Nörlund summability method. Here, almost generalized Nörlund summability method is considered. In 1913, Hardy [1] established (c,α), α> 0 summability o