Fixed point theorems in ordered abstract spaces

By J. J. Nieto, Rodrigo López Pouso, Rosana Rodríguez-López. 2007

270 citations recorded by the source corpus.

We extend some fixed point theorems in L-spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2793c4c3ba033b04b0e99aa187736870016966a3

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Coupled fixed point, $F$-invariant set and fixed point of $N$-order (2010, background): “Recently, there is also a trend to weaken the requirement on contractive conditions by considering metric spaces and cone metric spaces endowed with partial order [1, 2, 3, 5, 13, 15, 16, 17, 18].”
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”
A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations (2011, unknown): “Many authors have studied this problem, for a small sample of such work, we refer the reader to works [4,6,9,21,22,27,30,38,42].”
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].”
Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces (2009, background): “Recently Bhaskar and Lakshmikantham [5], Nieto and Rodriguez-Lopez [27], Nieto, Pouso and Rodriguez-Lopez [28], Ran and Reurings [31], and Agarwal, El-Gebeily, and O’Regan [1] presented some new results for contractions in partially ordered metric spaces.”