Geodesic
A general implicit iteration for finding fixed points of nonexpansive mappings
Sahu, D. R.1 ; Kang, Shin Min2 ; Kumar, Ajeet1 ; Cho, Sun Young3
1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
2 Center for General Education, China Medical University, Taichung 40402, Taiwan;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea
3 Department of Mathematics, Gyeongsang National University, Jinju 52828, Korea
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5157-5168.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The aim of the paper is to construct an iterative method for finding the fixed points of nonexpansive mappings. We introduce a general implicit iterative scheme for finding an element of the set of fixed points of a nonexpansive mapping defined on a nonempty closed convex subset of a real Hilbert space. The strong convergence theorem for the proposed iterative scheme is proved under certain assumptions imposed on the sequence of parameters. Our results extend and improve the results given by Ke and Ma [Y. Ke, C. Ma, Fixed Point Theory Appl., 2015 (2015), 21 pages], Xu et al. [H. K. Xu, M. A. Alghamdi, N. Shahzad, Fixed Point Theory Appl., 2015 (2015), 12 pages], and many others.
DOI : 10.22436/jnsa.009.08.01
Classification : 47J25, 47H09
Keywords: Metric projection mapping, nonexpansive mapping, variational inequality, viscosity method, implicit rules.

Sahu, D. R. 1 ; Kang, Shin Min 2 ; Kumar, Ajeet 1 ; Cho, Sun Young 3

1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
2 Center for General Education, China Medical University, Taichung 40402, Taiwan;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea
3 Department of Mathematics, Gyeongsang National University, Jinju 52828, Korea 
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Sahu, D. R.; Kang, Shin Min; Kumar, Ajeet; Cho, Sun Young. A general implicit iteration for finding fixed points of nonexpansive mappings. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5157-5168. doi : 10.22436/jnsa.009.08.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.08.01/

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