Fixed point theorems in partially ordered metric spaces and applications

By T. Gnana Bhaskar, V. Lakshmikantham. 2006

1,505 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/af8a0d56f11272a593c4767d7c0a896e6e1b5018

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In Geometry and Topology

Citations in the corpus

Coupled best proximity point theorem in metric Spaces (2012, background): “Bhaskar and Laksmikantham [14] introduced the notion of mixed monotone mapping and proved some coupled fixed point theorems for mappings satisfying the mixed monotone property.”
Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces (2011, methodology): “Presented theorems extend many existing results in the literature, in particular, the results obtained by Bhaskar and Lakshmikantham [4], Lakshmikantham and Ćirić [10], and include several recent developments.”
Some Coincidence Point Theorems for Nonlinear Contraction in Ordered Metric Spaces (2011, background): “Ty = 1 16 x4 ∈ [ 0, 1 16 ] .”
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations (2012, background): “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].”
Multidimensional Fixed-Point Theorems in Partially Ordered Complete Partial Metric Spaces under ()-Contractivity Conditions (2013, background): “In a recent paper, Gnana Bhaskar and Lakshmikantham [2] introduced the concept mixed monotone property for contractive operators of the form F : X × X → X, where X is a partially ordered metric space, and then established some coupled fixed-point theorems.”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “There exist a vast literature concerning its various generalizations and extensions (see [1-45]).”
Some fixed point results for (α,β)-(ψ,Φ)-contractive mappings (2014, background): “The concept of coupled fixed points for certain mappings in ordered spaces was first introduced by Bhaskar and Lakshmikantham [19] and applied their results to study the existence and uniqueness of solutions for boundary value problems, while the concept of coupled coincidence and coupled common fix”
COUPLED FIXED POINT THEOREMS AND APPLICATIONS TO PERIODIC BOUNDARY VALUE PROBLEMS (2013, methodology): “The approach is based on the application presented in [2].”