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SOOCHOW JOURNAL OF MATHEMATICS

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




ON SOME DIFFERENCE SEQUENCES DEFINED

BY A SEQUENCE OF ORLICZ FUNCTIONS


BY


AHMAD H. A. BATAINEH




Abstract. In this paper, we define the new difference sequence spaces: $ \omega_{_0}^{^\theta}(M_i, p, u,
s)_{\Delta^n}$, $ \omega^{^\theta}(M_i, p, u, s)_{\Delta^n}$ and $ \omega_{_\infty}^{^\theta}(M_i, p, u, s)_{\Delta^n}$, where $ u=(u_i)$ is any sequence such that $ u_i\neq 0(i=1, 2, \ldots)$. 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.