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)
Iterative equations in Banach spaces. (English) Zbl 1069.47064

This article deals with equations of type

i A i f i (x)=F(x)and i A i f(ϕ i (x))=F(x),

f i (·)(i=1,2, are iterations of f(·)). Both types are special cases of the equation 𝒫f=F with an operator 𝒫:𝒦(X)𝒦(X), where 𝒦(X)={f:XX Lipschitz:f-id sup <}. The authors present some theorems about the unique solvability of such equations; their proofs are based on the accurate calculation of the Lipschitz constant for the operator 𝒫-I and the application of the Banach-Caccioppoli fixed point principle.

47H10Fixed point theorems for nonlinear operators on topological linear spaces