In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to de...

We study geometric parameters associated with the Banach spaces (IRn, ‖·‖k,q) normed by ‖x‖k,q = (∑ 1≤i≤k |〈x, ai〉| )1/q , where {ai}i≤N is a given sequence of N points in IRn, 1 ≤ k ≤ N , 1 ≤ q ≤ ∞ and {λi }i≥1 denotes the decreasing rearrangement of a sequence {λi}i≥1 ⊂ IR. ∗

* Correspondence: [email protected] Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Full list of author information is available at the end of the article Abstract Recently, the concepts of statistical convergence, ideal convergence and lacunary statistical convergence have been studied in intuitionistic fuzzy normed spaces. In this article, we study the concepts ...

In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

We show that there are uncountably many geodesics between any two non-isometric $n$-dimensional normed spaces. construct explicit can be used to describe all the points of other geodesics.

One proves that the Mazur-Ulam theorem can be extended in the framework of metric spaces as long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur-Ulam space. Besides the classical case of real normed spaces, other examples such as Sym++(n,R), the space of all n × n dimensional positive definite matrices, appear as cones attached to suitable Euclidean Jo...

In this paper, we prove the stability of the functional equation ∑ 1 i, j n,i = j ( f (xi + x j)+ f (xi − x j) ) = (n−1) n ∑ i=1 ( 3 f (xi)+ f (−xi) ) in non-Archimedean normed spaces. Mathematics subject classification (2010): 39B82, 46S10, 39B52.

A blend of matrix summability and Euler transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties this space finally, some inclusion relations are presented.

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...