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)
Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. (English) Zbl 1220.54025

The purpose of this paper is to present, in the context of an ordered metric space, some fixed point theorems for continuous, nondecreasing mappings which satisfy Caristi type conditions with perturbed metrics. For example, the following theorem is proved.

Theorem 2.1. Let (X,) be a partially ordered set and suppose that there exists a metric d in X such that (X,d) is a complete metric space. Let f:XX be a continuous and nondecreasing mapping such that


where ψ,ϕ: + + are some altering distance functions. If there exists x 0 X with x 0 f(x 0 ), then f has a fixed point in X.

As an application, an existence result for a first-order periodic problem for a differential equation is given.

54H25Fixed-point and coincidence theorems in topological spaces
54F05Linearly, generalized, and partial ordered topological spaces
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34B15Nonlinear boundary value problems for ODE