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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 (β) and the uniform Opial property which is equipped with the Luxemburg norm. Finally, we show that this space has the fixed point property.

Some geometric properties of generalized modular sequence space derived by the generalized de la Vallée-Poussin mean