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)
Fixed point theory for cyclic Berinde operators. (English) Zbl 1237.54057
Summary: Inspired by the considerations in [{\it W. A. Kirk}, {\it P. S. Srinivasan} and {\it P. Veeramani}, Fixed Point Theory 4, No. 1, 79--89 (2003; Zbl 1052.54032)], which were further discussed in [{\it I. A. Rus}, “Cyclic representations and fixed points”, Ann. T. Popoviciu Seminar Funct. Eq. Approx. Convexity 3, 171--178 (2005)], we establish the existence and uniqueness of the fixed point for cyclic strict Berinde operators. Following [{\it I. A. Rus}, Fixed Point Theory 9, No. 2, 541--559 (2008; Zbl 1172.54030)], we build a so-called theory of the main result, referring concepts and phenomena like Picard operators, data dependence, limit shadowing, well-posedness of the fixed point problem. A Maia type result for cyclic strict Berinde operators is also given.

54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces
Full Text: Link