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)
Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization. (English) Zbl 0883.47063
Summary: A generalized “measure of distance” defined by $D_f(x,y):= f(x)- f(y)-\langle\nabla f(y),x- y\rangle$, is generated from any member $f$ of the class of Bregman functions. Although it is not, technically speaking, a distance function, it has been used in the past to define and study projection operators. In this paper, we give new definitions of paracontractions, convex combinations, and firmly nonexpansive operators, based on $D_f(x,y)$, and study sequential and simultaneous iterative algorithms employing them for the solution of the problem of finding a common asymptotic fixed point of a family of operators. Applications to the convex feasibility problem, to optimization and to monotone operator theory are also included.

47H09Mappings defined by “shrinking” properties
47H05Monotone operators (with respect to duality) and generalizations
90C25Convex programming
Full Text: DOI