Inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps

In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita...

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Bibliographic Details
Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2018; no. 1; pp. 1 - 9
Main Authors: Chidume, C. E., Ikechukwu, S. I., Adamu, A.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 12.03.2018
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Differential Geometry
Generalised projection
Inertial algorithm
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Relatively nonexpansive maps
Strong convergence
Topology
Strong convergence
47H09
Relatively nonexpansive maps
47J05
47H05
47J25
Inertial algorithm
Generalised projection
ISSN:1687-1812, 1687-1812
Online Access:Get full text
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Summary:In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita and Takahashi (J. Approx. Theory 134:257–266, 2005 ) and the result of Dong et al. (Optim. Lett. 12:87–102, 2018 ). Finally, we give some applications of our theorem.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-018-0634-3