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

Rabah Belbaki; Erdal Karapinar; Amar Ould-Hammouda,

doi:10.4995/agt.2018.10213

Authors

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

DOI:

https://doi.org/10.4995/agt.2018.10213

Keywords:

fixed point, Krasnoselskii iteration, monotone mapping, Reich type λâˆ’α-nonexpansive mapping, optial property

Abstract

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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