Geometry of linear 2-normed spaces pdf files

Topological properties of some sequences defined over 2normed. The notion of linear 2normed spaces was introduced by s. Wis clearly a linear subspace of xcontaining y, therefore the span of y is contained in w. The most standard example for a linear 2 normed space is x r2 equipped with the following 2norm, kx 1. In 1922, he defined normed linear spaces as a set of axioms. Pdf topological structure of 2normed space and some results. Geometry of linear 2normed spaces nova science, hauppauge, ny, 2001. This is true only for reallinear spaces, and is proved by characterizing the midpoint of a segment in a normed space in terms of the distance function. For nonzero vectors x,y in x, let vx,y denote the subspace of x generated by x and y. Pdf on contraction mappings and fixed point theorems in.

Full text of eudoxus press journals internet archive. Hereafter, we shall assume that dimx 3 unless otherwise stated. Gahler 8,9,10,11, and these space have been extensively studied by c. Some geometric remarks concerning strictly 2convex 2normed. An historical survey of the geometry of banach spaces with a more complete bibliography is given in cudia 1. The concept of iconvergence is a generalization of statistical convergence and it is depended on the notion of the ideal i of subsets of the set n of positive integers.

All of what follows takes place in a real normed linear space denoted by x or in the dual or conjugate space x of continuous linear functions on x. The concept of linear 2normed spaces has been investigated by gahler in. The primary purpose of this paper is to introduce the notion of fuzzy nnormed linear space as a generalization of nnormed space. Pdf linear mappings on linear 2normed spaces researchgate.