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.

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.

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...