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)
Viscosity approximation methods for mean non-expansive mappings in Banach spaces. (English) Zbl 1215.47100
Summary: Let $C$ be a nonempty closed convex subset of a real reflexive Banach space $X$ that has a weakly continuous duality mapping $J$. Let $T: C\to C$ be a mean nonexpansive mapping with $\text{Fix}(T)=\emptyset$. Let $f: C\to C$ be a contractive mapping. Then, for any $t\in(0,1)$, there exists an element $\{x_t\} \in C$ satisfying $$x_t=tf(x_t)+(1-t)Tx_t.$$ It is proved that $\{x_t\}\in C$ converges strongly to a fixed point of $T$ which is also a solution of a certain variational inequality.
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties