[PDF] Top 20 Approximate best proximity pairs in metric space for contraction maps

... the best proximity points of the sets A and B, by considering a map T : A ∪ B → A ∪ B such that T (A) ⊆ B and T (B) ⊆ ...A. Best proximity pair also evolves as a generalization of the concept ... See full document

... D-metric space was introduced in 1992 by Dhage [2] as an attempt to generalize the existing metric space ...D-metric space, annulling the validity of the majority of results that ... See full document

... of contraction condition for a pair of maps (S, T) in metric ...of best proximity points of such maps in the setting of uniformly convex Banach ...of best proximity ... See full document

... find best proximity pairs between two subsets of a met- ric space with a partial ...a metric space (X, d). A mapping S : A −→ B realizes the best proximity pair (x, ... See full document

... Theorem 3.1. Let M be a hyperconvex metric space and X be a nonempty admissible subset of M. Let F : X M be a Hausdorff continuous condensing set-valued map with nonempty bounded externally hyperconvex ... See full document

... quadruple best proximity points of Q-cyclic contraction pairs under the contractive conditions analogous to those used in ...The maps are defined on abstract metric spaces having ... See full document

... a metric space (X, d) and T a mapping from A to ...a best proximity theorem offers sufficient conditions for the existence of an element x, called a best proximity point of the ... See full document

... a metric space, a normed linear space, a topologi- cal vector space or some suitable ...an approximate solution x in A such that the error d(x, Tx) is minimum, where d is the distance ... See full document

... Banach Contraction Principle [4] is very familiar theorem that helps out in the branch of fixed point theory to describe the tools for finding a solu- tion to non-linear equations of the type U x = x if given ... See full document

... a metric space, a normed linear space, a topological vector space or some suitable ...an approximate solution x in A such that the error d(x, Tx) is minimum, where d is the distance ... See full document

... Corollary 2.5. Let M, d be a hyperconvex metric space. Let A ⊆ M be a nonempty compact admissible and let B be a nonempty subset of M. Let G : A A be a continuous, onto set-valued map with compact values ... See full document

... a metric space and let Aand B be nonempty subsets of ...a best proximity pair for F with respect to g if dga, Fa dA, B, where dA, B inf{da, b : a ∈ A, b ∈ ...B}. Best proximity ... See full document

... One of the most interesting is the study of the extension of Banach contraction princi- ple to the case of non-self-mappings. In fact, given nonempty closed subsets A and B of a complete PM-space (X, F, ∗), ... See full document

... In , Banach proved that every contractive mapping in a complete metric space has a unique fixed point, which is called Banach’s fixed point theorem or Banach’s contraction principle. Since Banach’s ... See full document

... a best prox- imity point theorem offers sufficient conditions for the existence of an element x, called a best proximity point of the mapping T , satisfying the condition that d(x, Tx) = d(A, ...that ... See full document

... of best approximation in the setting of complex valued metric ...certain best approximation results whichextend and generalize various known results of ordinary metric ... See full document

... for all x, y ∈ X, then T has at least one fixed point, that is, there exists z ∈ X such that z ∈ T z. In 2003, Kirk, Srinavasan and Veeramani [17] introduced a concept of cyclic contraction which generalized ... See full document

... Stability of fixed point sets of multivalued mappings was initially investigated by Markin [] and Nadler [] with some strong conditions. Lim [] proved the stability theorem for fixed point sets of multivalued ... See full document

... taking the limit as n → + ∞ , we deduce d(z, Tz) = d(A, B), because of the continuity of T . Finally we prove the uniqueness of the point x ∈ A such that d(x, Tx) = d(A, B). In- deed, suppose that there exist x, y ∈ A ... See full document

... of metric transforms which implies that a map- ping g : X → X is a local radial ...radial contraction. Theorem . Let (X, d) be a metric space and g : X → ...a metric transform φ on X ... See full document