Sahu, D. R.; Ansari, Q. H.; Yao, J. C. Convergence of inexact Mann iterations generated by nearly nonexpansive sequences and applications. (English) Zbl 1367.47071 Numer. Funct. Anal. Optim. 37, No. 10, 1312-1338 (2016). Summary: The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become efficiently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature. Cited in 9 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H06 Nonlinear accretive operators, dissipative operators, etc. Keywords:accretive operator; Mann iteration method; nearly Lipschitzian mapping; nonexpansive mapping; resolvent operator; split feasibility problem PDFBibTeX XMLCite \textit{D. R. Sahu} et al., Numer. Funct. Anal. Optim. 37, No. 10, 1312--1338 (2016; Zbl 1367.47071) Full Text: DOI References: [1] Agarwal R. P., Fixed Point Theory for Lipschitzian-Type Mappings with Applications 6 (2009) · Zbl 1176.47037 [2] Ansari Q. H., Taiwan. J. Math. 7 pp 1321– (2013) [3] DOI: 10.1080/00036811.2013.809067 · Zbl 1524.47079 · doi:10.1080/00036811.2013.809067 [4] J. B. Baillon and R. E. Bruck (1996). The rate of asymptotic regularity isTheory and Applications of Nonlinear Operators of Accretive and Monotone Types. Lecture Notes in Pure and Applied Mathematics, Vol. 178. Dekker, New York, pp. 51–81. · Zbl 0865.47038 [5] DOI: 10.1002/mana.200310003 · Zbl 1028.65060 · doi:10.1002/mana.200310003 [6] DOI: 10.1007/BF02762776 · Zbl 0475.47037 · doi:10.1007/BF02762776 [7] DOI: 10.1088/0266-5611/18/2/310 · Zbl 0996.65048 · doi:10.1088/0266-5611/18/2/310 [8] DOI: 10.1007/s11117-012-0174-8 · Zbl 1336.65100 · doi:10.1007/s11117-012-0174-8 [9] DOI: 10.1088/0266-5611/21/6/017 · Zbl 1089.65046 · doi:10.1088/0266-5611/21/6/017 [10] DOI: 10.1016/j.jmaa.2006.05.010 · Zbl 1253.90211 · doi:10.1016/j.jmaa.2006.05.010 [11] DOI: 10.1080/01630563.2014.930483 · Zbl 1314.47104 · doi:10.1080/01630563.2014.930483 [12] DOI: 10.1109/97.895371 · doi:10.1109/97.895371 [13] DOI: 10.1007/s11856-013-0045-4 · Zbl 1297.47074 · doi:10.1007/s11856-013-0045-4 [14] Goebel K., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings (1984) [15] DOI: 10.1017/CBO9780511526152 · doi:10.1017/CBO9780511526152 [16] DOI: 10.1090/S0002-9939-1974-0336469-5 · doi:10.1090/S0002-9939-1974-0336469-5 [17] DOI: 10.1016/j.jmaa.2006.05.009 · Zbl 1110.47057 · doi:10.1016/j.jmaa.2006.05.009 [18] DOI: 10.1090/S0002-9939-1953-0054846-3 · doi:10.1090/S0002-9939-1953-0054846-3 [19] Sahu D. R., Comment. Math. Univ. Carolinae 46 (4) pp 653– (2005) [20] DOI: 10.1007/s10898-012-9929-9 · Zbl 1297.90158 · doi:10.1007/s10898-012-9929-9 [21] DOI: 10.1155/2011/754702 · Zbl 1214.49009 · doi:10.1155/2011/754702 [22] DOI: 10.1137/100798648 · Zbl 1262.47091 · doi:10.1137/100798648 [23] DOI: 10.1006/jmaa.1993.1309 · Zbl 0895.47048 · doi:10.1006/jmaa.1993.1309 [24] DOI: 10.1090/S0002-9939-1994-1203993-5 · doi:10.1090/S0002-9939-1994-1203993-5 [25] DOI: 10.1016/0362-546X(91)90200-K · Zbl 0757.46033 · doi:10.1016/0362-546X(91)90200-K [26] DOI: 10.1112/S0024610702003332 · Zbl 1013.47032 · doi:10.1112/S0024610702003332 [27] DOI: 10.1088/0266-5611/22/6/007 · Zbl 1126.47057 · doi:10.1088/0266-5611/22/6/007 [28] DOI: 10.1088/0266-5611/20/4/014 · Zbl 1066.65047 · doi:10.1088/0266-5611/20/4/014 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.