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In this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L 1 ([0,1]). Our results generalize and unify the several related results in the literature.

On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])