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)
Iterative solution of $0\in Ax$ for an $m$-accretive operator $A$ in certain Banach spaces. (English) Zbl 1016.47045
The aim of the present article is to prove that the iteration process suggested in [{\it R. E. Bruck jun.}, J. Math. Anal. Appl. 48, 114-126 (1974; Zbl 0288.47048)] converges strongly to a zero of an $m$-accretive map in certain real Banach spaces, being more general than Hilbert spaces.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
WorldCat.org
Full Text: DOI
References:
[1] Browder, F. E.: Nonlinear monotone and accretive operators in Banach space. Proc. natl. Acad. sci. USA 61, 388-393 (1968) · Zbl 0167.15205
[2] Ishikawa, S.: Fixed points by a new iteration method. Proc. amer. Math. soc. 44, 147-150 (1974) · Zbl 0286.47036
[3] Mann, W. R.: Mean value methods in iteration. Proc. amer. Math. soc. 4, 506-510 (1953) · Zbl 0050.11603
[4] Chidume, C. E.; Mutangadura, S.: An example on the Mann iteration method for Lipschitzian pseudocontractions. Proc. amer. Math. soc. 129, 2359-2363 (2001) · Zbl 0972.47062
[5] Xu, Z. B.; Roach, G. F.: Characteristic inequalities for uniformly convex and uniformly smooth Banach spaces. J. math. Anal. appl. 157, 189-210 (1991) · Zbl 0757.46034
[6] Qihou, Liu: On naimpally and singh’s open question. J. math. Anal. appl. 124, 157-164 (1987) · Zbl 0625.47044
[7] Chidume, C. E.; Moore, C.: Fixed point iteration for pseudocontractive maps. Proc. amer. Math. soc. 127, 1163-1170 (1999) · Zbl 0913.47052
[8] Qihou, Liu: The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings. J. math. Anal. appl. 148, 55-62 (1990) · Zbl 0729.47052
[9] J. Schu, Approximating fixed points of Lipschitz pseudocontractive mappings, RWTH Aachen, Lehrstuhl C für Mathematik, Preprint No. 17 (1989)
[10] Chidume, C. E.: Iterative approximation of fixed points of Lipschitz pseudocontractive maps. Proc. amer. Math. soc. 129, 2245-2251 (2001) · Zbl 0979.47038
[11] Jr., R. E. Bruck: A strongly convergent iterative method for the solution of $0\inUx $for a maximal monotone operator U in Hilbert space. J. math. Anal. appl. 48, 114-126 (1974)
[12] Halpern, B.: Fixed points of nonexpansive maps. Bull. amer. Math. soc. 3, 957-961 (1967) · Zbl 0177.19101
[13] Cioranescu, I.: Geometry of Banach spaces, duality mapping and nonlinear problems. (1990) · Zbl 0712.47043
[14] Reich, S.: Strong convergent theorems for resolvents of accretive operators in Banach spaces. J. math. Anal. appl. 75, 287-292 (1980) · Zbl 0437.47047
[15] Fitzpatrick, P. M.; Hess, P.; Kato, T.: Local boundedness of monotone type operators. Proc. Japan acad. 48, 275-277 (1972) · Zbl 0252.47057