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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 223-244

Concepts of generalized bounded variation and the theory of Fourier series

Univerzitet “Dzemal Bijedić”, Gradjevinski fakultet, A. Zuanića 14, Mostar 88000, Serbia and Montenegro

Received 26 April 1985

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this article is to unify a large part of present knowledge about the behaviour of Fourier series of functions of generalized bounded variation. The connections between various concepts are discussed, particular attention being payed to those due to Waterman and Chanturiya. Exploiting the existing interactions and utilizing the power of one or another approach to some typical questions of the Fourier theory, a number of previously unnoticed results are obtained in the course of this exposition.