Ćirić, Łjubomir; Ume, Jeong Sheok Iterative processes with errors for nonlinear equations. (English) Zbl 1071.47061 Bull. Aust. Math. Soc. 69, No. 2, 177-189 (2004). Let \(D\) be a nonempty subset of a Banach space \(X\) and \(T:D \to 2^X\) be a multivalued operator of generalized monotone type such that \(T(D)\) is bounded and \(F(T):= \{x \in D | x \in T(x)\}\) is nonempty. Some new convergence theorems for the Ishikawa and Mann iteration processes with errors to a fixed point of \(T\) are given. Reviewer: Ioan A. Rus (Cluj-Napoca) Cited in 3 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H04 Set-valued operators 47H10 Fixed-point theorems Keywords:multivalued operator; Ishikawa iterations; Mann iterations; generalized monotone operator PDFBibTeX XMLCite \textit{Ł. Ćirić} and \textit{J. S. Ume}, Bull. Aust. Math. Soc. 69, No. 2, 177--189 (2004; Zbl 1071.47061) Full Text: DOI References: [1] DOI: 10.1016/0362-546X(94)00282-M · Zbl 0941.47039 · doi:10.1016/0362-546X(94)00282-M [2] DOI: 10.1016/0362-546X(94)00115-X · Zbl 0827.47041 · doi:10.1016/0362-546X(94)00115-X [3] DOI: 10.2307/2159893 · Zbl 0802.47058 · doi:10.2307/2159893 [4] Chidume, Bull. Austral. Math. Soc. 42 pp 21– (1990) [5] DOI: 10.1080/00036818608839641 · Zbl 0597.47039 · doi:10.1080/00036818608839641 [6] DOI: 10.1016/S0362-546X(97)00388-X · Zbl 0901.47036 · doi:10.1016/S0362-546X(97)00388-X [7] DOI: 10.1006/jmaa.1998.5993 · Zbl 0933.47040 · doi:10.1006/jmaa.1998.5993 [8] Chang, Bull. Austral. Math. Soc. 57 pp 433– (1998) [9] DOI: 10.1073/pnas.61.2.388 · Zbl 0167.15205 · doi:10.1073/pnas.61.2.388 [10] Zeidler, Nonlinear functional analysis and its applications. Part II. Monotone operators (1985) · Zbl 0583.47051 · doi:10.1007/978-1-4612-5020-3 [11] DOI: 10.1006/jmaa.1993.1287 · Zbl 0834.47048 · doi:10.1006/jmaa.1993.1287 [12] DOI: 10.1006/jmaa.1996.0203 · Zbl 0860.65039 · doi:10.1006/jmaa.1996.0203 [13] DOI: 10.1006/jmaa.1996.0461 · Zbl 0882.47030 · doi:10.1006/jmaa.1996.0461 [14] Osilike, Bull. Austral. Math. Soc. 46 pp 411– (1992) [15] DOI: 10.2307/2036395 · Zbl 0202.10103 · doi:10.2307/2036395 [16] DOI: 10.1006/jmaa.1995.1289 · Zbl 0872.47031 · doi:10.1006/jmaa.1995.1289 [17] DOI: 10.1090/S0002-9939-00-05807-X · Zbl 0973.47024 · doi:10.1090/S0002-9939-00-05807-X [18] DOI: 10.1016/0022-1236(78)90018-6 · Zbl 0422.47033 · doi:10.1016/0022-1236(78)90018-6 [19] DOI: 10.1006/jmaa.1995.1185 · Zbl 0868.47040 · doi:10.1006/jmaa.1995.1185 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.