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Some geometric inequalities in a new Banach sequence space. (English) Zbl 1132.46012
Summary: The difference sequence space $m(\varphi ,p,\Delta ^{(r)^{}})$, which is a generalization of the space $m(\varphi )$ introduced and studied by {\it W. L. C. Sargent} [J. Lond. Math. Soc. 35, No. 2, 161--171 (1960; Zbl 0090.03703)], was defined by {\it R. Çolak} and {\it M. Et} [Bull. Malays. Math. Sci. Soc. (2) 28, No. 2, 125--130 (2005)]. In this paper, we establish some geometric inequalities for this space.

##### MSC:
 46B45 Banach sequence spaces
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##### References:
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