In 1964, Gähler 1 introduced the concept of 2-norm and 2-inner product spaces as generalization of norm and inner product spaces. A systematic presentation of the results related to the theory of 2-inner product spaces can be found in the book in 2, 3 and in list of references in it. Generalization of 2-inner product space for n ≥ 2 was developed by Misiak 4 in 1989. Gunawan and Mashadi 5 in 20...

In this paper we introduce the sequence spaces χM (p, q, u), using an modulus function M and defined over a semi normed space (X, q), semi normed by q. We study some properties of these sequence spaces and obtain some inclusion relations.

Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆-statistical convergence and lacunary ∆-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. Subjclass [2000] : Primary 40A05; Secondary 46A70, 40A99, 46A99.

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces

We study computability on sequence spaces, as they are used in functional analysis. It is known that non-separable normed spaces cannot be admissibly represented on Turing machines. We prove that under the Axiom of Choice non-separable normed spaces cannot even be admissibly represented with respect to any compatible topology (a compatible topology is one which makes all bounded linear function...

The main purpose of this paper is to study normed hypervector spaces. We generalize some definitions such as basis, convexity, operator norm, closed set, Cauchy sequences, and continuity in such spaces and prove some theorems about them.

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...

We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...