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


  • Rabah Belbaki Laboratory of Physics Mathematics and Applications
  • Erdal Karapinar Atilim University https://orcid.org/0000-0002-6798-3254
  • Amar Ould-Hammouda, Laboratory of Physics Mathematics and Applications




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


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.


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Author Biography

Erdal Karapinar, Atilim University

Department of Mathematics


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How to Cite

R. Belbaki, E. Karapinar, and A. Ould-Hammouda, “On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])”, Appl. Gen. Topol., vol. 19, no. 2, pp. 291–305, Oct. 2018.