On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces
By Syed Abdul Mohiuddine, Abdullah Alotaibi. 2012
384 citations recorded by the source corpus.
Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4fc3ce9238401f24e0a23e15cdd8ec6b8da5b2f7
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Citations in the corpus
- Nonlinear contractions in metric spaces under locally $T$-transitive binary relations (2015, background): “The following family of control functions is introduced by Lakshmikantham and Ćirić [4].”
- Fixed point results on metric and partial metric spaces via simulation functions (2015, background): “However, the potentiality of fixed point approaches attracted many scientists and hence there is a wide literature available for interested readers, see for instance [3, 7, 8, 9, 11, 18, 20, 21, 24, 25, 27].”
- Nonlinear contractions involving simulation functions in a metric space with a partial order (2015, result): “Further, several results appeared in this direction, we mention [1, 2, 3, 4, 5, 7, 8, 9, 10, 13] and the references therein.”
- 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”