in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

we study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesx_{i}. we introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by x boxtimesy. we investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

We introduce the operation L copulative with T,L to define PN space under T,L and establish some basic properties of probabilistic seminorms and norms under T,L Finally, we discuss so-called L-simple spaces.

In this work, our purpose is to introduce I−convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I−convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I−convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed s...

In this paper, we obtain a characterization of linear spaces which may be normed so as to become complete, linear, normed metric spaces. In this connection, K. Kunugui and M. Fréchet have shown that every metric space S is isometric with a subset of a complete, linear, normed metric space. I t follows from our result that if the cardinal number of 5 is the limit of a denumerable sequence of car...

Let |·| be the standard Euclidean norm on ℝ n and let X=(ℝ ,∥·∥) a normed space. A subspace Y⊂X is strongly α-Euclidean if there constant t such that t|y|≤∥y∥≤αt|y| for every y∈Y, say it α-complemented ∥P Y ∥≤α, where P orthogonal projection from X to ∥ denotes operator of with respect X. We give an example space arbitrarily high dimension 2-Euclidean but contains no 2-dimensional both (1+ϵ)-Eu...