zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Coupled fixed points in partially ordered metric spaces and application. (English) Zbl 1202.54036
Summary: We prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7 (A), 1379–1393 (2006; Zbl 1106.47047)]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
45G10Nonsingular nonlinear integral equations
References:
[1]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 (2004) · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[2]Bhaskar, T. Gnana; Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. TMA 65, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[3]Nieto, J. J.; Rodriguez-Lopez, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order 22, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[4]Nieto, J. J.; Rodriguez-Lopez, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. Sin. (Engl. Ser.) 23, No. 12, 2205-2212 (2007) · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[5]Agarwal, R. P.; El-Gebeily, M. A.; O’regan, D.: Generalized contractions in partially ordered metric spaces, Appl. anal. 87, 1-8 (2008) · Zbl 1140.47042 · doi:10.1080/00036810701556151
[6]Lakshmikantham, V.; Ćirić, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. TMA 70, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[7]Samet, B.: Coupled fixed point theorems for a generalized Meir–Keeler contraction in partially ordered metric spaces, Nonlinear anal. TMA (2010)
[8]Altun, I.; Simsek, H.: Some fixed point theorems on ordered metric spaces and application, Fixed point theory appl. 2010 (2010) · Zbl 1197.54053 · doi:10.1155/2010/621469
[9]Harjani, J.; Sadarangani, K.: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear anal. TMA 72, 1188-1197 (2010) · Zbl 1220.54025 · doi:10.1016/j.na.2009.08.003