Abstract The article focuses on the introduction of neutrosophic continuity and boundedness, which is a fair extension intuitionistic fuzzy respectively. further advances to illustrate Fréchet derivative nonlinear operators between normed spaces (NNS). Examples have been provided in compliance with theory aid some standard sequence spaces.

In this paper, we introduce the concept of λ-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and λ-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, λ)-summability in n-normed spaces.

In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed spaces.

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.