Add to ORKGSankar Raj and P. Veeramani Abstract. Let A,B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T: A∪B → A∪B be a map such that T (A) ⊆ B, T (B) ⊆ A and ‖Tx − Ty ‖ ≤ ‖x − y‖, for x in A and y in B. The fixed point equation Tx = x does not possess a solution when A ∩ B = ∅. In such a situation it is natural to explore to find an element x0 in A satisfying ‖x0 − Tx0 ‖ = inf{‖a − b ‖ : a ∈ A, b ∈ B} = dist(A,B). Using Zorn’s lemma, Eldred et.al proved that such a point x0 exists in a uniformly convex Banach space settings under the conditions stated above. In this paper, by using a convergence theorem we attempt to prove the existence of such a point x0 (called best proximity point) without invoking Zorn’s l...
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using ...
Abstract Every non-convex pair ( C , D ) $(C, D)$ may not have proximal normal structure even in a H...
A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A i...
Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → ...
[EN] Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A...
Given that A and B are two nonempty subsets of the convex metric space (X,d,W), a mapping T:A∪B→A∪B ...
Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to b...
Let A and B be nonempty subsets of a Banach space X and T :&...
A new class of noncyclic mappings, called generalized noncyclic relatively nonexpansive, is introduc...
AbstractIn this manuscript, we proved that the existence of best proximity points for the cyclic ope...
Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively non...
In this article, we survey the existence, uniqueness and convergence of a common best proximity poin...
Abstract. The purpose of this article is to generalized the result of W. S-intunavarat and P. Kumam ...
The purpose of this article is to generalized the result of W. Sintunavarat and P. Kumam [29]. We al...
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using ...
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using ...
Abstract Every non-convex pair ( C , D ) $(C, D)$ may not have proximal normal structure even in a H...
A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A i...
Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → ...
[EN] Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A...
Given that A and B are two nonempty subsets of the convex metric space (X,d,W), a mapping T:A∪B→A∪B ...
Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to b...
Let A and B be nonempty subsets of a Banach space X and T :&...
A new class of noncyclic mappings, called generalized noncyclic relatively nonexpansive, is introduc...
AbstractIn this manuscript, we proved that the existence of best proximity points for the cyclic ope...
Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively non...
In this article, we survey the existence, uniqueness and convergence of a common best proximity poin...
Abstract. The purpose of this article is to generalized the result of W. S-intunavarat and P. Kumam ...
The purpose of this article is to generalized the result of W. Sintunavarat and P. Kumam [29]. We al...
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using ...
In this paper we prove existence theorems of best proximity pairs in uniformly convex spaces, using ...
Abstract Every non-convex pair ( C , D ) $(C, D)$ may not have proximal normal structure even in a H...
A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A i...