Inertial Krasnoselskii–Mann Method in Banach Spaces

Yekini Shehu and Aviv Gibali
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Yekini Shehu: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Aviv Gibali: Department of Mathematics, ORT Braude College, 2161002 Karmiel, Israel

Mathematics, 2020, vol. 8, issue 4, 1-13

Abstract: In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q -uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.

Keywords: Krasnoselskii–Mann; nonexpansive mapping; forward-backward splitting method; q-uniformly smooth; Banach spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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