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Journal of Scientific Computing

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01.01.2021

Inertial-Type Algorithm for Solving Split Common Fixed Point Problems in Banach Spaces

verfasst von: A. Taiwo, L. O. Jolaoso, O. T. Mewomo

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

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Abstract

In this paper, motivated by the works of Kohsaka and Takahashi (SIAM J Optim 19:824–835, 2008) and Aoyama et al. (J Nonlinear Convex Anal 10:131–147, 2009) on the class of mappings of firmly nonexpansive type, we explore some properties of firmly nonexpansive-like mappings [or mappings of type (P)] in p-uniformly convex and uniformly smooth Banach spaces. We then study the split common fixed point problems for mappings of type (P) and Bregman weak relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an inertial-type shrinking projection algorithm for solving the two-set split common fixed point problems and prove a strong convergence theorem. Also, we apply our result to the split monotone inclusion problems and illustrate the behaviour of our algorithm with several numerical examples s. The implementation of the algorithm does not require a prior knowledge of the operator norm. Our results complement many recent results in the literature in this direction. To the best of our knowledge, it seems to be the first to use the inertial technique to solve the split common fixed point problems outside Hilbert spaces.

Vorheriger Artikel A Level Set Method for the Dirichlet k-Partition Problem

Nächster Artikel A Second-Order Corrector Infeasible Interior-Point Method for Semidefinite Optimization Based on a Wide Neighborhood

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Titel: Inertial-Type Algorithm for Solving Split Common Fixed Point Problems in Banach Spaces
verfasst von: A. Taiwo
L. O. Jolaoso
O. T. Mewomo
Publikationsdatum: 01.01.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01385-9

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