This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

In this paper we established some of the results of the best simultaneous approximation in the context of linear 2-normed space. 2000 Mathematics Subject Classification: 41A50, 41A52, 41A99, 41A28.

Let X be a Banach space, (I, μ) be a finite measure space, and Φ be an increasing subadditive continuous function on [0,+∞) with Φ(0) = 0. In the present paper, we discuss the best p-simultaneous approximation of L(I,G) in L(I,X) where G is a closed subspace of X .

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

the main purpose of this paper is to find t-best approximations in fuzzy normed spaces. we introduce the notions of t-proximinal sets and f-approximations and prove some interesting theorems. in particular, we investigate the set of all t-best approximations to an element from a set.

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.