zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Approximating fixed points of nonexpansive mappings in a Banach space by metric projections. (English) Zbl 1190.47072
Summary: A strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem is different from the recent strong convergence theorem due to {\it H.-K.\thinspace Xu} [Bull. Aust. Math. Soc. 74, No. 1, 143--151 (2006; Zbl 1126.47056)] which was established by generalized projections.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Alber, Y. I.: Metric and generalized projection operators in Banach spaces: properties and applications. Lecture notes in pure and applied mathematics, 15-50 (1996) · Zbl 0883.47083
[2] Browder, F. E.: Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces. Arch. ration. Mech. anal. 24, 82-90 (1967) · Zbl 0148.13601
[3] Bruck, R. E.: On the convex approximation property and the asymptotic behaviour of nonlinear contractions in Banach sapces. Israel J. Math. 38, 304-314 (1981) · Zbl 0475.47037
[4] Cioranescu, I.: Geometry of Banach spaces, duality mappings and nonlinear problems. (1990) · Zbl 0712.47043
[5] Halpern, B.: Fixed points of nonexpanding maps. Bull. am. Math. soc. 73, 957-961 (1967) · Zbl 0177.19101
[6] Matsushita, S.; Takahashi, W.: A strong convergence theorem for relatively nonexpansive mappings in a Banach space. J. approx. Theory 134, 257-266 (2005) · Zbl 1071.47063
[7] Nakajo, K.; Takahashi, W.: Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. math. Anal. appl. 279, 372-379 (2003) · Zbl 1035.47048
[8] Pascali, D.; Sburlan, S.: Nonlinear mappings of monotone type. (1978) · Zbl 0423.47021
[9] Reich, S.: Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. math. Anal. appl. 75, 287-292 (1980) · Zbl 0437.47047
[10] Shioji, N.; Takahashi, W.: Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces. Proc. am. Math. soc. 125, 3641-3645 (1997) · Zbl 0888.47034
[11] Takahashi, W.: Convex analysis and approximation fixed points. (2000) · Zbl 1089.49500
[12] Takahashi, W.: Nonlinear functional analysis. Fixed points theory and its applications. (2000) · Zbl 0997.47002
[13] Takahashi, W.; Ueda, Y.: On reich’s strong convergence theorems for resolvents of accretive operators. J. math. Anal. appl. 104, 546-553 (1984) · Zbl 0599.47084
[14] Wittmann, R.: Approximation of fixed points of nonexpansive mappings. Arch. math. 58, 486-491 (1992) · Zbl 0797.47036
[15] Xu, H. K.: Strong convergence of approximating fixed point sequences for nonexpansive mappings. Bull. aust. Math. soc. 74, 143-151 (2006) · Zbl 1126.47056