We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset Ω⊂RN and a Banach space V, we characterize the functions in Sobolev-Reshetnyak R1,p(Ω,V), where 1≤p≤∞, terms existence partial metric derivatives or w⁎-derivatives suitable integrability properties. In case p=∞ R1,∞(Ω,V) is characterized uniform local Lipschitz property. also consider special V=ℓ∞.

We analyze the injective deformations on Lipschitz domains, motivated by the configurations of solid elastic materials. Our goal is to rigorously derive the first order optimality conditions when minimizing over deformations with a self-contact constraint. In a previous work, we established a variational equation for minimizers of a second-gradient hyper-elastic energy. This involved obtaining ...

In a recent work, thanks to the use of Cliiord algebras and designants, we have shown that Wynn's vector "-algorithm can be written as a ratio of two designants. The present work, according to these new results, has the aim of 1. Finding easily and diierently the results of some authors in this scope, particularly those of Wynn, D.E. Roberts and P.R. Graves-Morris. 2. Computing explicitly the e...

We prove that some important properties of convex subsets of vector topological spaces remain valid in the space of fuzzy numbers endowed with the Euclidean distance. We use these results to obtain a characterization of fuzzy number-valued Lipschitz functions. This fact helps us to find the best Lipschitz constant of the trapezoidal approximation operator preserving the value and ambiguity intr...

Abstract In this article, without requiring solidness of the underlying cone, a kind new convergence for sequences in cone b b -metric spaces over Banach algebras and completeness such spaces, namely, wrtn-completeness, are introduced. Under condition that wrtn-complete cones normal, we establish common fixed point the...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

1. Topological Vector Spaces 1 1.1. The Krein-Milman theorem 7 2. Banach Algebras 11 2.1. Commutative Banach algebras 14 2.2. ∗–Algebras (over complexes) 17 2.3. Problems on Banach algebras 20 3. The Spectral Theorem 21 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 26 3.2. Integration with respect to a Projection Valued Measure 27 3.3. The Functional Calculus 34 4. Unboun...