Bounded linear functional on nnormed spaces through its quotient spaces. For nonzero vectors x,y in x, let vx,y denote the subspace of x generated by x and y. An historical survey of the geometry of banach spaces with a more complete bibliography is given in cudia 1. Some of the basic properties of 2norms, they are nonnegative and kx. Topological properties of some sequences defined over 2normed. Pdf in this paper we construct the topological structure of linear.
Unfortunately, in the standard 2normed space which is also the standard 2inner product space, one cannot. The most standard example for a linear 2 normed space is x r2 equipped with the following 2norm, kx 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. Some properties of accretive operators in linear 2normed. However, banach was the pioneer of formal functional analysis.
The primary purpose of this paper is to introduce the notion of fuzzy nnormed linear space as a generalization of nnormed space. 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. Pdf on contraction mappings and fixed point theorems in. 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.
A complete 2normed space e is called 2banach space. If z is any linear subspace containing y, then z must contain w, therefore \ z contains w. Hereafter, we shall assume that dimx 3 unless otherwise stated. Pdf topological structure of 2normed space and some results. In 1922, he defined normed linear spaces as a set of axioms. Some geometric remarks concerning strictly 2convex 2normed.