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)
Generalized projection algorithms for nonlinear operators. (English) Zbl 1132.47048
Let E be a reflexive and strictly convex and smooth Banach space, C a closed convex subset of E, T a selfmap of C with F(T) denoting the fixed point set of T. A point p in C is said to be an asymptotic fixed point of T if C contains a sequence {x n } that converges weakly to p and is such that the strong limit of (Tx n -x n ) is 0. The set of asymptotic fixed points is denoted by F ^(T). T is called relatively nonexpansive if F(T)=F ^(T) and ϕ(p,Tx)ϕ(p,x) for each pF(T) and xC, where ϕ(x,y):=x 2 -2x,j(y)+y 2 . T is called relatively asymptotically nonexpansive if F(T)=F ^(T) and ϕ(x,T n x)k n ϕ(p,x) for each xC, pF(T). With E a uniformly convex and uniformly smooth Banach space, and using a complicated iteration scheme involving duality maps and their inverses, the authors obtain the strong convergence to a fixed point of T for T either strictly relatively nonexpansive or relatively asymptotically nonexpansive, provided that F(T).
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
47H10Fixed point theorems for nonlinear operators on topological linear spaces