Fixed point theorems for generalized contractions in ordered metric spaces

By Donal O'Regan, Adrian Petrusel. 2008

390 citations recorded by the source corpus.

Abstract The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435–1443], J.J. Nieto, R. Rodriguez-Lopez [J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; J.J. Nieto, R. Rodriguez-Lopez, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205–2212], J.J. Nieto, R.L. Pouso, R. Rodriguez-Lopez [J.J. Nieto, R.L. Pouso, R. Rodriguez-Lopez, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505–2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L -spaces, Proc. Amer. Math. Soc. 134 (2006) 411–418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d4040b93f1e05b38b2ee35484c730df3c1c361ce

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

Citations in the corpus

A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations (2012, background): “The existence of a fixed point, a common fixed point and a couple fixed point for some kinds of contraction type mappings in cone metric spaces, partially ordered metric spaces and fuzzy metric spaces has been considered recently by some authors [1-28] and, by using fixed point theorems, some of the”
SOME FIXED POINT RESULTS IN ORDERED PARTIAL METRIC SPACES (2011, result): “ n. If there exists x0 ∈ Xwith x0 ≤X fx0, then fhas a ﬁxed point. Many other results on the existence of ﬁxed points or common ﬁxed points in ordered metric spaces were given, we can cite for example [1, 3, 5, 6, 7, 9, 12, 15, 21, 23] and the references therein. 1 2 H. AYDI In this paper we extend t”
Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces (2010, background): “Theorem 1 was further extended and refined in [18, 19, 16, 20, 21].”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “Using this lemma, he proved that some very recent fixed-point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [15] and Amini-Harandi and Emami [5] do follow from an earlier result of O’Regan and Petruşel [29, Theorem 3.6].”
Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “Existence of fixed point in partially ordered sets has been considered recently in [24–28].”
Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces (2011, background): “Afterward, coupled fixed point and common fixed point theorems and their applications to periodic boundary value problems and integral equations were given in [5-7,12-19].”