Moch. Aruman Imron
Let sine series defined on [0,2π]. It is shown that if (α,β) in p-supremum bounded variation sequences and n1-1/psupm≥b(n)∑2mk=βk=0(1) for 1=≤p<∞, with a=(an) is sequence of coefficients of sine series, (b(n))⊂[0,∞) tending monotonically to infinity depending only on (an), and β=(βn) is sequence of real non-negatif, then the sine series converges uniformly on [0,2π]. We weaken this condition to so called generalized difference sequence of p-supremum bounded variation sequences and study the properties that class. It will be shown that uniform convergence of sine and cosine series under that class is fulfilled. © 2015 Moch. Aruman Imron.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia
