In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...

The story begins with the paper of Müller, [59], who — for the sake of an application to nonlinear elasticity — proved that if the Jacobian determinant Ju of a Sobolev map u ∈ W 1,n loc (Rn ,Rn ) is nonnegative, then it belongs locally to L log L. The result is quite intriguing, since a priori Hölder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability. If one ...

We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension—the so called Clifford space (C-space), a manifold of points, lines, areas, etc..; physical quantities are Clifford algebra valued objects , called polyvectors. This provides a natural framework for description of super-symmetry, since spinors are just left or right ...

In this paper we present inequalities for integrals of functions that are the composition of nonnegative convex functions on an open convex set of a vector space R and vectorvalued functions in a weakly compact subset of a Banach vector space generated by m Lμ-spaces for 1 ≤ p < +∞ and inequalities when these vector-valued functions are in a weakly* compact subset of a Banach vector space gener...

The concept of the lower limit for vector-valued mappings is the main focus of this work. We first introduce a new definition of adequate lower and upper level sets for vector-valued mappings and establish some of their topological and geometrical properties. Characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define the concept of vector lower limit,...

Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).However, most of them are single-valued measures and lack of potential for efficiency validation.In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.The vector is defined as a two-tuple consisting of ...

In this letter, we provide a study of learning in a Hilbert space of vectorvalued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a repr...

This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both themapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to ha...