in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

In this paper we formulate the notions of simultaneously remotal and that of simultaneously densely remotal sets. We exhibit large classes of Banach spaces which have subspaces, whose unit ball is a simultaneously remotal set. We also study them in spaces of vectorvalued function spaces.

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 be a Banach space and E be a closed bounded subset of X. For x ∈ X we set D(x,E) = sup{‖x− e‖ : e ∈ E}. The set E is called remotal in X if for any x ∈ X, there exists e ∈ E such that D(x,E) = ‖x− e‖ . It is the object of this paper to give new results on remotal sets in L(I,X), and to simplify the proofs of some results in [5].

Let X be a Banach space and let G be a closed bounded subset of X. For x1, x2, . . . , xm ∈ X, we set ρ x1, x2, . . . , xm,G sup{max1≤i≤m‖xi−y‖ : y ∈ G}. The setG is called simultaneously remotal if, for any x1, x2, . . . , xm ∈ X, there exists g ∈ G such that ρ x1, x2, . . . , xm,G max1≤i≤m‖xi−g‖. In this paper, we show that if G is separable simultaneously remotal in X, then the set of ∞Bochn...

let $(x, n)$ be a fuzzy normed space and $a$ be a fuzzy boundedsubset of $x$.  we define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. then we will show that in these spaces, all  fuzzyuniquely remotal sets are singletons.

Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$.  We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all  fuzzyuniquely remotal sets are singletons.

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.