zbMATH — the first resource for mathematics

Strong convergence of an iterative method with perturbed mappings for nonexpansive and accretive operators. (English) Zbl 1140.47050
Summary: A new iterative method for finding a zero of $$m$$-accretive operators is proposed. This method, involving a so-called perturbed mapping, provides a way to construct sunny nonexpansive retractions. Several strong convergence theorems for this method are established in a Banach space that is either uniformly smooth or reflexive with a weakly continuous duality map.

MSC:
 47J25 Iterative procedures involving nonlinear operators 47H06 Nonlinear accretive operators, dissipative operators, etc. 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 47H14 Perturbations of nonlinear operators
Full Text:
References:
 [1] Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces (1976) · Zbl 0328.47035 [2] Browder F.E., Proc. Natl. Acad. Sci. USA 53 pp 1272– (1965) · Zbl 0125.35801 [3] Browder F.E., Math. Z. 100 pp 201– (1967) · Zbl 0149.36301 [4] Browder F.E., J. Math. Anal. Appl. 20 pp 197– (1967) · Zbl 0153.45701 [5] Dominguez Benavides T., Math. Nachr. 248 pp 62– (2003) · Zbl 1028.65060 [6] Goebel K., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mapping (1984) [7] Jung J.S., Nonlinear Anal. 46 pp 231– (2001) · Zbl 0997.47042 [8] Lim T.C., Nonlinear Anal. 22 pp 1345– (1994) · Zbl 0812.47058 [9] Marino G., Comm. Pure Appl. Anal. 3 pp 791– (2004) · Zbl 1095.90115 [10] Reich S., J. Math. Anal. Appl. 75 pp 287– (1980) · Zbl 0437.47047 [11] Reich S., J. Funct. Anal. 36 pp 147– (1980) · Zbl 0437.47048 [12] Xu H.K., J. London Math. Soc. 66 pp 240– (2002) · Zbl 1013.47032 [13] Xu H.K., J. Optim. Theory Appl. 116 pp 659– (2003) · Zbl 1043.90063 [14] Xu H.K., J. Math. Anal. Appl. 314 pp 631– (2006) · Zbl 1086.47060 [15] Zeng L.C., Taiwanese J. Math. 10 pp 87– (2006) [16] Zeng L.C., Nonlinear Anal. 64 pp 2507– (2006) · Zbl 1105.47061
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.