Researchers have identified and defined β- approach normed space if some conditions are satisfied. In this work, we show that every is a space.However, the converse not necessarily true by giving an example. addition, define β – Banach space, examples given. We also solve problems. discuss finite β-dimensional app-normed β-complete consequent app- space. explain metric but give propositions. If...

Abstract. Generalizing Pisier’s idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten class. In general, a pair of symmetric normed ideals that are not necessarily the Schatten class may give rise to an operator space...

‎In 1897‎, ‎Hensel introduced a normed space which does‎ ‎not have the Archimedean property‎. ‎During the last three decades‎ ‎theory of non--Archimedean spaces has gained the interest of‎ ‎physicists for their research in particular in problems coming‎ ‎from quantum physics‎, ‎p--adic strings and superstrings‎. ‎In this paper‎, ‎we prove‎ ‎the generalized Hyers--Ulam--Rassias stability for a‎ ...

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...

in this paper, using the fixed point and direct methods, we prove the generalized hyers-ulam-rassias stability of the following cauchy-jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. the concept of hyers-ulam-rassias stability originated from th. m. rassias’ stability theorem t...

Discrete versions of Ostrowski’s inequality for vectors in normed linear spaces are given.

In [6], the second author proved general metatheorems for the extraction of effective uniform bounds from ineffective existence proofs in functional analysis, more precisely from proofs in classical analysis A(:= weakly extensional Peano arithmetic WE-PA in all finite types + quantitifer-free choice + the axiom schema of dependent choice DC) extended with (variants of) abstract bounded metric s...