Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations

By J. J. Nieto, Rosana Rodríguez-López. Order, 2005

1,458 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2dbce4fc6199ff95305e4a7bfeba869b779921f3

How researchers see this paper

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

In Applied Mathematics

1. Ravi P. Agarwal
2. Ljubomir Ciric
3. Bessem Samet
4. Donal O'Regan
5. J. J. Nieto
6. Vasile Berinde
7. Wasfi A. Shatanawi
8. Bapurao C. Dhage

In Geometry and Topology

1. Bessem Samet
2. E. Karapınar
3. Ljubomir Ciric
4. Hassen Aydi
5. Ravi P. Agarwal
6. Vasile Berinde
7. Calogero Vetro
8. Wasfi A. Shatanawi

In Numerical Analysis

1. Ravi P. Agarwal
2. Donal O'Regan
3. Bessem Samet
4. Ljubomir Ciric
5. E. Karapınar
6. Bapurao C. Dhage
7. Mohammad Imdad
8. Aftab Alam

Citations in the corpus

• 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.”
• Generalized contractions in metric spaces endowed with a graph (2012, background): “Rodríguez-López [19] proved a modified variant of Theorem 1.”
• Relation-theoretic metrical coincidence theorems (2016, background): “[7] J. J. Nieto and R. Rodŕıguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (3) (2005) 223-239.”
• Nonlinear contractions in metric spaces under locally $T$-transitive binary relations (2015, methodology): “The following notion is formulated by using a suitable property with a view to avoid the necessity of the continuity requirement on the involved mapping specially in the hypotheses of a fixed point theorem due to Nieto and Rodŕıguez-López [8].”
• Common fixed point results for new Ciric-type rational multivalued F-contraction with an application (2018, background): “Fixed point theorems for operators in ordered metric spaces are widely investigated and have found various applications in differential and integral equations (see [4,18,24,28] and references therein).”
• 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].”
• Various Suzuki type theorems in b -metric spaces (2015, background): “For more details on fixed point results, their applications, comparison of different contractive conditions and related results in ordered metric spaces and spaces endowed with a graph we refer the reader to [5] and [19].”
• 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 point theorems on ordered metric spaces and applications to nonlinear elastic beam equations (2012, result): “Presented theorems extend and generalize several existing results in the literature, including the works of Ran and Reurings [19], Nieto and López [16], Bhaskar and Lakshmikantham [8] and Berinde [7].”