In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...

Let (X,N) be a fuzzy normed space. For each 0 < < 1 and a non-empty subset A of X, we define a natural notion for -farthest points from A and a set-valued map x 7→ Q (A, x), called the fuzzy -farthest point map. Then we will investigate basic properties of the fuzzy -farthest point mapping. In particular, we show that the fuzzy -farthest point map is closable.

We prove some results on the farthest points in convex metric spaces and in linear metric spaces. The continuity of the farthest point map and characterization of strictly convex linear metric spaces in terms of farthest points are also discussed.

In this paper, we give a complete description of the farthest point map, as defined on regular octahedron with its intrinsic flat cone metric. As consequence show that every well-defined orbit map converges to 1-skeleton barycentric subdivision triangulation.

In this paper, we first present some sufficient conditions for the upper semicontinuity and/or the continuity of the Bregman farthest-point map QgC and the relative farthest-point map S g C for a nonempty D-maximally approximately compact subset C of a Banach space X. We next present certain sufficient conditions as well as equivalent conditions for a Klee set to be singleton in a Banach space ...

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

in this paper, using the best proximity theorems for an extensionof brosowski&apos;s theorem. we obtain other results on farthest points. finally, wedene the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

In this paper, we prove that if E is an uniquely remotal subset of a real normed linear space such has Chebyshev center c ∈ and the farthest point map F : → restricted to [c, (c)] p...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...