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

Rabah Belbaki, Erdal Karapinar, Amar Ould-Hammouda,


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 L1([0,1]). Our results generalize and unify the several related results in the literature.


fixed point; Krasnoselskii iteration; monotone mapping; Reich type λ−α-nonexpansive mapping; optial property

Subject classification

46T99; 47H10; 54H25

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