zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings. (English) Zbl 1097.47057
Summary: Several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [{\it B.--L. Xu} and {\it M. A. Noor}, J. Math. Anal. Appl. 267, No. 2, 444--453 (2002; Zbl 1011.47039); {\it Y. J. Cho, H.--Y. Zhou} and {\it G.--T. Guo}, Comput. Math. Appl. 47, No. 4--5, 707--717 (2004; Zbl 1081.47063)], and many others.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
WorldCat.org
Full Text: DOI
References:
[1] Chidume, C. E.; Moore, C.: Fixed points iteration for pseudocontractive maps. Proc. amer. Math. soc. 127, No. 4, 1163-1170 (1999) · Zbl 0913.47052
[2] Cho, Y. J.; Zhou, H.; Guo, G.: Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings. Comput. math. Appl. 47, 707-717 (2004) · Zbl 1081.47063
[3] Das, G.; Debata, J. P.: Fixed points of quasi-nonexpansive mappings. Indian J. Pure appl. Math. 17, 1263-1269 (1986) · Zbl 0605.47054
[4] Khan, S. H.; Un-Din, H. F.: Weak and strong convergence of a scheme with errors for two nonexpansive mappings. Nonlinear anal. 61, 1295-1301 (2005) · Zbl 1086.47050
[5] Maiti, M.; Gosh, M. K.: Approximating fixed points by Ishikawa iterates. Bull. austral. Math. soc. 40, 113-117 (1989) · Zbl 0667.47030
[6] Mann, W. R.: Mean value methods in iterations. Proc. amer. Math. soc. 4, 506-510 (1953) · Zbl 0050.11603
[7] Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. amer. Math. soc. 733, 591-597 (1967) · Zbl 0179.19902
[8] Schu, J.: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bull. austral. Math. soc. 43, 153-159 (1991) · Zbl 0709.47051
[9] Senter, H. F.; Dotson, W. G.: Approximating fixed points of nonexpansive mappings. Proc. amer. Math. soc. 44, No. 2, 375-380 (1974) · Zbl 0299.47032
[10] S. Suantai, Weak and strong convergence criteria of Noor iteration for asymptotically nonexpansive mappings, J. Math. Anal. Appl., in press · Zbl 1086.47057
[11] Takahashi, W.; Tamura, T.: Convergence theorems for a pair of nonexpansive mappings. J. convex anal. 5, No. 1, 45-58 (1998) · Zbl 0916.47042
[12] Tan, K. K.; Xu, H. K.: Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. J. math. Anal. appl. 178, 301-308 (1993) · Zbl 0895.47048
[13] Xu, Y.: Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations. J. math. Anal. appl. 224, 91-101 (1998) · Zbl 0936.47041
[14] Xu, B. L.; Noor, M. A.: Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces. J. math. Anal. appl. 267, 444-453 (2002) · Zbl 1011.47039