A general implicit iteration for finding fixed points of nonexpansive mappings
Authors
D. R. Sahu
 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India.
Shin Min Kang
 Center for General Education, China Medical University, Taichung 40402, Taiwan.
 Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea.
Ajeet Kumar
 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India.
Sun Young Cho
 Department of Mathematics, Gyeongsang National University, Jinju 52828, Korea.
Abstract
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.
Share and Cite
ISRP Style
D. R. Sahu, Shin Min Kang, Ajeet Kumar, Sun Young Cho, A general implicit iteration for finding fixed points of nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 8, 51575168
AMA Style
Sahu D. R., Kang Shin Min, Kumar Ajeet, Cho Sun Young, A general implicit iteration for finding fixed points of nonexpansive mappings. J. Nonlinear Sci. Appl. (2016); 9(8):51575168
Chicago/Turabian Style
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 Applications, 9, no. 8 (2016): 51575168
Keywords
 Metric projection mapping
 nonexpansive mapping
 variational inequality
 viscosity method
 implicit rules.
MSC
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