; Aust. J. Math. Anal. Appl. Vol. 18 (2021), No. 1, Art. 3, 6 pp. AJMAA SOME PROPERTIES OF COSINE SERIES WITH COEFFICIENTS FROM CLASS OF GENERAL MONOTONE SEQUENCES ORDER r CORINA KARIM, MOCH. ARUMAN IMRON * Received 24 February, 2020; accepted 15 October, 2020; published 11 January, 2021. DEPARTMENT OF MATHEMATICS,UNIVERSITAS BRAWIJAYA,I NDONESIA. co_mathub@ub.ac.id maimr@ub.ac.id * ABSTRACT. The coefficient of sine series from general monotone class has been generalized by Bogdan Szal to the new class which is called class of general monotone order r. This coefficient class is more general than class of general monotone introduced by Tikhonov. By special case, we study properties of cosine series with coefficient of sine series from the class of general monotone order r. Key words and phrases: Cosine series; Coefficient of sine series; Monotone class. 2000 Mathematics Subject Classification. Primary 40A05; Secondary 12A20,46A45. ISSN (electronic): 1449-5910 c 2021 Austral Internet Publishing. All rights reserved. The authors gratefully acknowledge the support of Faculty of Mathematics and Sciences, University of Brawijaya, chair and friends from department of Mathematics. * Corresponding Author.