Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

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

681 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/beb848a4e031f0352d6982393ee326bb37a65ed0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Fixed point results for multivalued contractions on a metric space with a graph (2013, background): “Later, their results were generalized to maps not necessarily monotone but which are such that the images of comparable points are comparable [10,12].”
Generalized contractions in metric spaces endowed with a graph (2012, background): “Rodríguez-López [20], where some interesting applications to ordinary differential equations with periodic boundary conditions are also given.”
Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces (2011, result): “Following basically the same approach as the one in [8], and unifying the results in [6] and [7], Bhaskar and Lakshmikantham [3] obtained some coupled fixed point results for mixed monotone operators F : X ×X → X which satisfy a certain contractive type condition, where X is a partially ordered metr”
Relation-theoretic contraction principle (2015, background): “Here, it is fascinating to point out that corresponding theorems contained in [10, 19, 2, 17, 18, 12, 11, 5, 13] cannot be used in the context of the foregoing examples (i.”
Coupled fixed points in partially ordered metric spaces and application (2011, background): “The existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems are presented in [8,2,9,3,4,1].”
Monotone generalized contractions in partially ordered probabilistic metric spaces (2009, methodology): “The main idea in [2-11] involve combining the ideas of iterative technique in the contraction mapping principle with those in the monotone technique.”