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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Vydané v:	Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2018; číslo 1; s. 1 - 9
Hlavní autori:	Chidume, C. E., Ikechukwu, S. I., Adamu, A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 12.03.2018 SpringerOpen
Predmet:	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
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Popis
Shrnutí:	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