Search

The aim of this paper is to study relationships among 'gauge integrals' (Henstock, McShane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose, we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems (Theorems 3.2, 4.2, 5.3). As applications of such decompositions, we deduce characterizations of Henstock (Theorem 3.3) and $$\mathcal H$$ (Theorem 4.3) integrable multifunctions, together with an extension of a well-known theorem of Fremlin [22, Theorem 8]. [ABSTRACT FROM AUTHOR]

Some convergence theorems have been obtained for the GHk integral for functions defined in abstract topological spaces and with values in Riesz spaces. [ABSTRACT FROM AUTHOR]

In this paper we outline a new theory about integral and differential calculus for Riesz space-valued mappings defined on suitable Riesz spaces. In our abstract context, we prove some theorems similar to the classical ones, like for example the Fundamental Formula of Calculus and the theorem about exchanging order between limits and derivatives. As applications, we give some results about power series, a fixed point theorem, and some models of differential functional equations. [ABSTRACT FROM AUTHOR]

In this paper we formulate a version of the Kondurar theorem and a generalization of the Itô formula for functions taking values in Riesz spaces with respect to a convergence, satisfying suitable axioms. When the involved space is the space of measurable functions, both convergence almost everywhere and convergence in probability are included. Finally we present some comments and possible applications of the Itô formula. [ABSTRACT FROM AUTHOR]

The literature examining primary headache, including migraine, in adolescents, has pointed out the key role played by a wide range of psychiatric disorders in reducing the patients' quality of life. Moreover, pioneering studies showed that preexisting personality characteristics, specific emotion regulation styles and psychological-psychiatric difficulties are likely to increase the risk of the onset, maintenance, and outcome of headache. Still personality issues in migraine have been poorly studied, in particular in children and adolescents. This study aims, therefore, to investigate the specific characteristics of personality, and in particular emotion regulation and coping strategies, in adolescent with migraine, comparing them with age-matched patients with idiopathic epilepsy and healthy adolescents. 52 adolescents (age: 11-17) were assessed using a multi-method test battery, which included a self-report questionnaire (the youth self-report), a proxy-report (child behavior checklist) along with a projective personality test, the Rorschach Test, administered and scored according to the Exner comprehensive system. The results showed specific personality characteristics in adolescents with migraine, revealing a marked difficulty in modulating and regulating affections through thoughts and reflections, resorting instead to impulsive acts and maladaptive coping strategies, thus revealing a vague and immature perception of reality. Differently from adolescents belonging to the general population, but similarly to patients with epilepsy, adolescents with migraine perceive a high situational stress, probably related to the condition of suffering from chronic disease. They have, therefore, a lower self-consideration and self-esteem along with a poorer insight regarding themselves as well as the relations with others. In line with previous findings, these preliminary results suggest the need for further research on ample samples, using also standardized projective test in order to better understand the pathogenesis of psychological difficulties in patients with migraine. As a clinical implication, the results seem to indicate that providing a psychological integrated approach can play a pivotal role in the assessment and treatment of adolescent with migraine, in order to improve the outcome and the quality of life of the young patients.