A fixed point theorem in partially ordered sets and some applications to matrix equations

By A. Ran, M. Reurings. 2003

1,577 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b0fa9cc53c4f8fc5f8d85f0ed0abfc57b1e63e7e

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

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”
Weak $F$-contractions and some fixed point results (2016, result): “Some fixed point results in ordered L-spaces that generalize and extend a result from [13] are proved by A.”
Generalized contractions in partially ordered metric spaces (2008, methodology): “This approach was initiated in [2] and the results in [1] are slight extensions of those in [2].”
Fixed Points for -Graphic Contractions with Application to Integral Equations (2013, background): “Fixed Point Results in Partially Ordered Partial Metric Spaces Fixed point theorems for monotone operators in partially orderedmetric spaces are widely investigated and have found various applications in differential and integral equations (see [24, 25] and references therein).”
Generalized contractions in metric spaces endowed with a graph (2012, background): “In 2004, Ran and Reurings [23] started a new research direction in fixed point theory by proving the following Banach–Caccioppoli type principle in ordered metric spaces.”
Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces (2011, methodology): “Besides, applications to matrix equations and ordinary differential equations were presented in [10,11].”
Nonlinear D-set contraction mappings in partially ordered normed linear spaces and applications to functional hybrid integral equations (2014, background): “We continue the study presented in Dhage [11], Nieto and Lopez [22] and Ran and Reurings [23] and prove some new hybrid fixed point theorems (FPTs) for partially condensing mappings in a partially ordered complete normed linear space and apply our abstract results to a certain nonlinear hybrid funct”
SOME FIXED POINT RESULTS IN ORDERED PARTIAL METRIC SPACES (2011, background): “When fixed point problems in partially ordered metric spaces are concerned, first results were obtained by Ran and Reurings [17], and then by Nieto and López [11].”
Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations (2007, methodology): “The new results are more general than the fixed point theorem presented in [1], since we have proved that it is possible to remove the hypotheses of continuity and monotonicity of function f , providing alternative conditions, some of them relative to the space X.”
Common fixed points of mappings satisfying implicit contractive conditions (2012, neutral): “Ran, ACM, Reurings, MC: A fixed point theorem in partially ordered sets and some applications to matrix equations.”