Often, about the same real-life system, we have both measurementrelated probabilistic information expressed by a probability measure P (S) and expert-related possibilistic information expressed by a possibility measure M(S). To get the most adequate idea about the system, we must combine these two pieces of information. For this combination, R. Yager – borrowing an idea from fuzzy logic – propo...

We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1. Preliminaries. 2. Sequence spaces. 3. Spaces of measurable functions. 4. Hardy spaces. 5. Banach algebras of holomorphic functions. 6. Fréchet algebras of holomorphic functions. 7. Spaces of continuous functions. In...

In this   paper,  we   present  some  refinements  of the   famous Young  type  inequality.   As  application  of   our   result, we  obtain  some  matrix inequalities   for   the  Hilbert-Schmidt norm  and   the  trace   norm. The results    obtained   in  this  paper  can  be   viewed   as  refinement  of  the   derived  results   by  H.  Kai  [Young  type  inequalities  for matrices,  J.  Ea...

We show that the fractional Sobolev inequality for the embedding H̊ s 2 (R ) →֒ L 2N N−s (R ), s ∈ (0, N) can be sharpened by adding a remainder term proportional to the distance to the set of optimizers. As a corollary, we derive the existence of a remainder term in the weak L N N−s -norm for functions supported in a domain of finite measure. Our results generalize earlier work for the non-fract...

Abstract We show that independent and uniformly distributed sampling points are asymptotically as good optimal for the approximation of functions from Sobolev spaces $W_p^s(\varOmega )$ on bounded convex domains $\varOmega \subset{\mathbb{R}}^d$ in $L_q$-norm if $q<p$. More generally, we characterize quality arbitrary point sets $P\subset \varOmega $ via $L_\gamma (\varOmega )$-norm dist...

We establish an integral formula for the duality between multilinear forms/homogeneous polynomials and tensor products for dual spaces with the approximation property and for which the injective tensor products of their preduals is separable and does not contain a copy of `1. We deduce some multilinear Bishop-Phelps-type results. Although spaces of multilinear forms and homogeneous polynomials ...