Qin, Xiaolong; Cho, Yeol Je; Kang, Shin Min Some results on non-expansive mappings and relaxed cocoercive mappings in Hilbert spaces. (English) Zbl 1204.47084 Appl. Anal. 88, No. 1, 1-13 (2009). Summary: We introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximation methods. Our results improve and extend the recent ones announced by H.Iiduka and W.Takahashi [Nonlinear Anal., Theory Methods Appl.61, No.3, A, 341–350 (2005; Zbl 1093.47058)] and many others. Cited in 3 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H05 Monotone operators and generalizations 47J20 Variational and other types of inequalities involving nonlinear operators (general) Keywords:projection method; relaxed cocoercive mapping; nonexpansive mapping; fixed point; variational inequality Citations:Zbl 1093.47058 PDFBibTeX XMLCite \textit{X. Qin} et al., Appl. Anal. 88, No. 1, 1--13 (2009; Zbl 1204.47084) Full Text: DOI References: [1] DOI: 10.1023/B:JOTA.0000026271.19947.05 · Zbl 1056.49017 · doi:10.1023/B:JOTA.0000026271.19947.05 [2] DOI: 10.1016/j.aml.2005.02.026 · Zbl 1099.47054 · doi:10.1016/j.aml.2005.02.026 [3] DOI: 10.1090/S0002-9947-1970-0282272-5 · doi:10.1090/S0002-9947-1970-0282272-5 [4] DOI: 10.1023/A:1025407607560 · Zbl 1055.47052 · doi:10.1023/A:1025407607560 [5] DOI: 10.1016/j.na.2003.07.023 · Zbl 1093.47058 · doi:10.1016/j.na.2003.07.023 [6] DOI: 10.1016/j.jmaa.2006.12.088 · Zbl 1137.47307 · doi:10.1016/j.jmaa.2006.12.088 [7] DOI: 10.1080/01630569808816813 · Zbl 0913.47048 · doi:10.1080/01630569808816813 [8] DOI: 10.1016/j.jmaa.2005.05.028 · Zbl 1095.47038 · doi:10.1016/j.jmaa.2005.05.028 [9] DOI: 10.1112/S0024610702003332 · Zbl 1013.47032 · doi:10.1112/S0024610702003332 [10] DOI: 10.1023/A:1023073621589 · Zbl 1043.90063 · doi:10.1023/A:1023073621589 [11] Yamada I, Inherently Parallel Algorithm for Feasibility and Optimization pp 473– (2001) · doi:10.1016/S1570-579X(01)80028-8 [12] DOI: 10.1137/S0036144593251710 · Zbl 0865.47039 · doi:10.1137/S0036144593251710 [13] DOI: 10.1109/5.214546 · doi:10.1109/5.214546 [14] DOI: 10.1006/jmaa.1996.0308 · Zbl 0956.47024 · doi:10.1006/jmaa.1996.0308 [15] Combettes PL, Proceedings of the IEEE International Conference on Image Processing pp 2025– (1995) [16] DOI: 10.1080/01630569408816580 · Zbl 0807.41019 · doi:10.1080/01630569408816580 [17] Youla DC, Image Recovery: Theory and Applications pp 29– (1987) [18] DOI: 10.1007/BF01582891 · Zbl 0744.90066 · doi:10.1007/BF01582891 [19] Atsushiba S, Indian J. Math. 41 pp 435– (1999) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.