| Kanagajothi Dharumaraj†, Selvaraj Chellachi Premila‡, Prabavathy Magadevan§, Saravanan Karpagam§
Abstract: Let A and B be non-empty subsets of a metric space (X,d). Let T : A ∪ B → A ∪ B be a map such that T(A) ⊆ B and T(B) ⊆ A satisfying a certain contractive condition called cyclic orbital proximal contraction. We give the necessary conditions for the existence of a unique point ξ ∈ A such that d(ξ,Tξ) is equal to the distance between A and B. Our main result generalizes the main result of [A.A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006]. Keywords: cyclic map, best proximity point, orbital contractions, uniformly convex Banach space. MSC: 47H10, 54H25. DOI 10.56082/annalsarscimath.2026.2.263 †kanagajothi82@gmail.com, Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R and D Institute of Science and Technology, Chennai, Tamilnadu, India |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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