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 theorems in partially ordered metric spaces and applications. (English) Zbl 1106.47047
This paper gives some coupled fixed point theorems for a monotone mapping in a metric space endowed with a partial order, using a weak contractivity type assumption. Besides including several recent developments, the theorems can be used to investigate a class of problems. As an application, the existence and uniqueness of solutions for a periodic boundary value problem are discussed.

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34B15Nonlinear boundary value problems for ODE
54H25Fixed-point and coincidence theorems in topological spaces
54F05Linearly, generalized, and partial ordered topological spaces
Full Text: DOI
[1] Gouze, J. -L.; Hadeler, K. P.: Monotone flows and order intervals. Nonlin. world 1, 23-34 (1994) · Zbl 0803.65076
[2] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045
[3] Heikkila, S.; Lakshmikantham, V.: Monotone iterative techniques for discontinuous nonlinear differential equations. (1994)
[4] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S.: Monotone iterative techniques for nonlinear differential equations. (1985) · Zbl 0658.35003
[5] Lakshmikantham, V.; Bhaskar, T. Gnana; Devi, J. Vasundhara: Theory of set differential equations in metric spaces. (2005) · Zbl 1156.34003
[6] Lakshmikantham, V.; Mohapatra, R. N.: Theory of fuzzy differential equations and inclusions. (2003) · Zbl 1072.34001
[7] Lakshmikantham, V.; Koksal, S.: Monotone flows and rapid convergence for nonlinear partial differential equations. (2003)
[8] J.J. Nieto, R.R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order (in press)
[9] J.J. Nieto, R.R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta. Math. Sinica (in press)
[10] Ran, A. C. M.; Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. amer. Math. soc. 132, 1435-1443 (2003) · Zbl 1060.47056
[11] Schroder, J.: Operator inequalities. (1980)