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Some geometric properties of generalized modular sequence space derived by the generalized de la Vallée-Poussin mean. (English) Zbl 1375.46019

Summary: In this paper, we define a generalized modular sequence space by using the generalized de la Vallée-Poussin mean with a generalized Riesz transformation. Moreover, we investigate the property \((\beta)\) and the uniform Opial property which is equipped with the Luxemburg norm. Finally, we show that this space has the fixed point property.

MSC:

46B45 Banach sequence spaces
46B20 Geometry and structure of normed linear spaces
40H05 Functional analytic methods in summability
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