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)
Weak convergence theorems for nonexpansive mappings and monotone mappings. (English) Zbl 1055.47052
Let $K$ be a closed convex subset of a real Hilbert space $H$, $A:K\rightarrow H$ be inverse strongly monotone, and $S:K\rightarrow K$ be nonexpansive. Assuming that the set of solutions of the variational inequality for $A$ and the set of fixed points of $S$ have a nonempty intersection, the authors introduce an iteration process that is shown to generate a sequence converging weakly to an element of this intersection. This is the main result of the paper, which is then applied to obtain a sequence converging to a common fixed point of a nonexpansive map and a strictly pseudocontractive map.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
55M20Fixed points and coincidences (algebraic topology)
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
Full Text: DOI