SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 761-769, October 2007

BY

AHMAD H. A. BATAINEH

Abstract. In this paper, we define the new difference sequence spaces: , and , where is any sequence such that . We also study some inclusion relations between these spaces. These are generalizations of those defined and studied by Bilgin [5].

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Received July 17, 2006; revised June 14, 2007.

AMS Subject Classification. 40A05, 40F05, 46A45.

*Key words*. difference sequence spaces, lacunary
sequence, a sequence of Orlicz functions.