We show that a separable proximinal subspace of X, say Y is strongly proximinal (strongly ball proximinal) if and only if Lp(I, Y ) is strongly proximinal (strongly ball proximinal) in Lp(I,X), for 1 ≤ p <∞. The p =∞ case requires a stronger assumption, that of ’uniform proximinality’. Further, we show that a separable subspace Y is ball proximinal in X if and only if Lp(I, Y ) is ball proximin...

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

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.