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 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...

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.

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].

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 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.

We show that every in nite dimensional Banach space has a closed and bounded convex set that is not remotal. This settles a problem raised by Sababheh and Khalil in [8].

In this paper, we study the Chebyshev centres of bounded subsets of normed spaces and obtain a norm inequality for relative centres. In particular, we prove that if T is a remotal subset of an inner product space H, and F is a star-shaped set at a relative Chebyshev centre c of T with respect to F, then llx - qT (x)1I2 2 Ilx-cll2 + Ilc-qT (c) 112 x E F, where qT : F + T is any choice functi...

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.