Coupled Best Proximity Points for Noncyclic Maps in Uniformly Convex Banach Spaces
Session
Computer Science and Communication Engineering
Description
This paper studies coupled best proximity points for noncyclic maps in uniformly convex Banach spaces. While classical fixed point theory is well-established for self-maps, cyclic maps, and coupled fixed points, noncyclic maps, especially those of two variables, remain less explored. We generalize the notions of optimal points, best proximity points, and coupled fixed points to noncyclic maps of two variables, introducing the concept of optimal pairs of coupled fixed points. We provide sufficient conditions for the existence and uniqueness of such points in uniformly convex Banach spaces with convex subsets separated by a positive distance. Additionally, we present both a priori and a posteriori error estimates for iterative approximations, which are essential for practical applications where exact solutions are unattainable. Our results extend classical fixed point theory and offer effective tools for approximation methods in mathematical modeling, optimization, and applied mathematics, paving the way for further research on coupled noncyclic mappings in complex systems.
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-982-41-2
Location
UBT Lipjan, Kosovo
Start Date
25-10-2025 9:00 AM
End Date
26-10-2025 6:00 PM
DOI
10.33107/ubt-ic.2025.97
Recommended Citation
Azemi, Laura Ajeti, "Coupled Best Proximity Points for Noncyclic Maps in Uniformly Convex Banach Spaces" (2025). UBT International Conference. 29.
https://knowledgecenter.ubt-uni.net/conference/2025UBTIC/CS/29
Coupled Best Proximity Points for Noncyclic Maps in Uniformly Convex Banach Spaces
UBT Lipjan, Kosovo
This paper studies coupled best proximity points for noncyclic maps in uniformly convex Banach spaces. While classical fixed point theory is well-established for self-maps, cyclic maps, and coupled fixed points, noncyclic maps, especially those of two variables, remain less explored. We generalize the notions of optimal points, best proximity points, and coupled fixed points to noncyclic maps of two variables, introducing the concept of optimal pairs of coupled fixed points. We provide sufficient conditions for the existence and uniqueness of such points in uniformly convex Banach spaces with convex subsets separated by a positive distance. Additionally, we present both a priori and a posteriori error estimates for iterative approximations, which are essential for practical applications where exact solutions are unattainable. Our results extend classical fixed point theory and offer effective tools for approximation methods in mathematical modeling, optimization, and applied mathematics, paving the way for further research on coupled noncyclic mappings in complex systems.