Isosceles constant in Banach spaces Baronti, Marco; Casini, Emanuele; Papini, Pier Luigi
Journal of mathematical analysis and applications,
08/2024, Letnik:
536, Številka:
1
Journal Article
Recenzirano
The rectangular constant in Banach spaces was introduced in a paper by N. Gastinel and J.L. Joly in 1970 and has also received attention recently. To define such a constant, the notion of ...orthogonality, according to Birkhoff and James, is used. Here, we introduce and study a similar constant, but based on isosceles orthogonality. We indicate several properties of the new constant as a characterization of Hilbert spaces and of uniformly non-square spaces. These characterizations are similar to those proven for the old constant. Some illustrative examples complete the paper.
The decline in children's vaccination coverage and the resurgence of preventable infectious diseases draw attention to parents' vaccine hesitancy. Our study introduces two validated tools to ...independently assess vaccine hesitancy and health literacy among parents with school-age children. We developed a Vaccine Confidence Index (VCI) from 10 Likert items, exploring their relationships through exploratory and confirmatory factor analyses. We modified the IMETER (Italian medical term recognition test) to measure health literacy. We assessed the internal consistency of the modified IMETER and the 10 Likert items using Cronbach's alpha test (α) and McDonald's omega total coefficient (ω) with good results (ω = 0.92, α = 0.90; ω = 0.87, α = 0.82 respectively). We used these tools within a questionnaire conducted on 743 parents recruited from pediatric clinic waiting rooms in Italy, collecting demographic data, information sources on vaccines and vaccine-preventable diseases knowledge. The VCI resulting from factor analyses consisted of six items on a ten-point Likert scale, reflecting the ratio of positive to negative items. The survey revealed significant variations in the VCI according to individual features such as education, use of social networks, or Health institutions as sources of information. Multivariate logistic regression identified an association between vaccine intention and the VCI. Health literacy was functional for 91.2% of participants, but knowledge about vaccine-preventable diseases was generally low. The VCI showed no significant association with health literacy and vaccine-preventable diseases knowledge. The VCI and the modified IMETER effectively assess vaccination attitude and health literacy, offering valuable public health tools for tailoring vaccination campaigns to hesitant population subgroups.
The present paper is related to the study of asymmetry for copulas by introducing functionals based
on different norms for continuous variables. In particular, we discuss some facts concerning ...asymmetry and
we point out some flaws occurring in the recent literature dealing with this matter.
We prove that in some classes of reflexive Banach spaces every maximal diametral set must be diametrically complete, thus showing that diametrically complete sets may have empty interior also in ...reflexive spaces. As a consequence, we prove that, in those spaces, normal structure is equivalent to the weaker property that, for every bounded set, the absolute Chebyshev radius is strictly smaller than the diameter. Moreover, we prove that, in any normed space, the two classes of diametrically complete sets and of sets of constant radius from the boundary coincide if the space has normal structure.
Nested sequences of stars and starshaped sets Baronti, Marco; Casini, Emanuele; Papini, Pier Luigi
Journal of mathematical analysis and applications,
09/2019, Letnik:
477, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper we consider nested (decreasing and increasing) sequences of stars or starshaped sets in Banach spaces. The intersection, if decreasing, and the closure of the union, if increasing, are ...studied with regards to the preservation of these properties. Among other results we show that the closure of an increasing sequence of stars is a star if and only if the sequence of their centers is weakly convergent. Similar results, for starshaped sets, are true exactly in reflexive spaces.
The notion of orthogonality for vectors in inner product spaces is simple, interesting and fruitful. As known, when moving to normed spaces, we have many possibilities to extend this notion in a way ...that the new notion of orthogonality reduces to the usual one when the norm is derived from an inner product. One of these possibilities was exploited by Roberts’ orthogonality. But, in a sense, it is too restrictive. Here we consider Birkhoff orthogonality and isosceles orthogonality, which are the most used notions of orthogonality, and study how “far” they are from orthogonality in the sense of Roberts. Related measurements of differences between pairs of orthogonality types are also studied.
Convexity, smoothness and moduli Baronti, Marco; Papini, Pier Luigi
Nonlinear analysis,
03/2009, Letnik:
70, Številka:
6
Journal Article
Recenzirano
Banaś defined a modulus for Banach spaces which has appeared in the literature, but not studied in details until now.
We point out several interesting properties of that modulus, and its relationship ...with other constants of Banach spaces.
The lattice-theoretic structure of the set of semi-copulas and some of its subsets is investigated. As a relevant case, we obtain that the set of commutative semi-copulas is a lattice completion of ...the set of triangular norms.
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