We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3-dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms...

We introduce a new norm on the space of all bounded linear operators complex Hilbert space, which generalizes numerical radius norm, usual operator and modified Davis–Wielandt norm. study basic properties this including upper lower bounds for it. As an application present study, we estimate operators. illustrate that our results improve some important existing inequalities. Other have also stud...

We prove that an asymmetric normed space is never a Baire if the topology induced by norm not equivalent to of norm. More precisely, we show biBanach and only it isomorphic its associated space.

When a class of fuzzy value functions constitute a metric space, the completeness and separability is an important problem that must be considered to discuss the approximation of fuzzy systems. In this paper, Firstly, a new tK-integral norm is defined by introducing two induced operators, and prove that the class of tK-integrable fuzzy value functions is a metric space. And then, the integral t...

Fuzzy anti-bounded linear functional and fuzzy antidual spaces are defined. Hahn-Banach theorem and some of its consequences on fuzzy anti-normed linear space are studied. Two fundamental theorems; namely, open mapping theorem and closed graph theorem are established. Keywords-Fuzzy anti-norm, α-norm, Fuzzy anti-complete, Fuzzy anti-bounded linear functional, Fuzzy anti-dual space.

(A revised and expanded version of these notes are now published by Springer.) 1 Banach Spaces Definition A normed vector space X is a vector space over R or C with a function called the norm. 1. The set of real numbers with the norm taken to be the absolute value.

The main purpose of this paper is to use the idea of n-norm and a modulus function to construct some multiplier sequence spaces with base space X, a real linear n-norm space. We study the spaces for linearity, existence of paranorm, completeness and some inclusion properties involving these spaces. Mathematics Subject Classification: 40A05, 46A45, 46E30

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an M-ideal in the space of bounded operators, a very smooth operator T attains its norm at a unique vector x (up to a constant multiple) and T (x) is a very smooth point of the range space. We show that if for every equivalent norm on a Ban...

s In respect of the de finition of intuitionistic fuzzy n-norm [9] , the definition of generalised intuitionistic fuzzy ψ norm ( in short GIFψN ) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy ψ normed linear space and finite dimensional generalized intuitionistic fuzzy ψ normed linear space have been developed. Lastly, we have introduced the...