1,721,004 research outputs found
A characterization of absolutely summing operators by means of McShane integrable functions
Full text linkIn [2] Diestel characterized absolutely summing operators between Banach
spaces by means of Pettis integrable strongly measurable functions. As the
class of Pettis integrable strongly measurable functions is a proper subset of
that of McShane integrable ones, it seems natural to ask if the analogous characterization
holds considering McShane integrable functions. In this lecture
the results about this characterization are presente
Riemann type integrals for functions taking values in a locally convex space
Full text linkThe McShane and Kurzweil-Henstock integrals for functions taking values
in a locally convex space are dened and the relations with other integrals are studied.
A characterization of locally convex spaces in which Henstock Lemma holds is given
On weakly measurable stochastic processes and absolutely summing operators
Full text linksummary:A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered
Strongly measurable Kurzweil-Henstock type integrable functions and series
No full textWe give necessary and sufficient conditions for the scalar Kurzweil-Henstock integrability and the Kurzweil-Henstock-Pettis integrability of functions defined as . Also the variational Henstock integrability is considere
The method of lower and upper solutions for second order periodic Stieltjes differential equations
Full text linkAs an application of the Schauder Fixed Point Theorem, an existence theory is developed for second order nonlinear differential equations with Stieltjes derivative related to a left-continuous, nondecreasing function. By the method of lower and upper solutions, under a Nagumo-type assumption we get a very general result which can be further applied to deduce the existence of solutions for second order nonlinear problems in the settings of impulsive differential equations, time scale analysis or generalized differential equations
Stieltjes differential problems with general boundary value conditions. Existence and bounds of solutions
No full textWe are concerned with first order set-valued problems with very general boundary value conditions involving the Stieltjes derivative with respect to a left-continuous nondecreasing function , a Carathéodory multifunction and a continuous . Using appropriate notions of lower and upper solutions, we prove the existence of solutions via a fixed point result for condensing mappings. In the periodic single-valued case, combining an existence theory for the linear case with a recent result involving lower and upper solutions (which can be seen as a consequence of our existence theorem mentioned before), we get not only the existence of solutions, but also lower and upper bounds, respectively, by imposing an estimation for the right-hand side
Convergence Theorems for Varying Measures Under Convexity Conditions and Applications
Full text linkIn this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or on the measures. Consequently, a continuous dependence result for a wide class of differential equations with many interesting applications, namely measure differential equations (including Stieltjes differential equations, generalized differential problems, impulsive differential equations with finitely or countably many impulses and also dynamic equations on time scales) is provided
Relaxation Theorem for Stieltjes Differential Inclusions on Infinite Intervals
Full text linkFor a very general first-order differential problem on an infinite-time horizon involving the Stieltjes derivative with respect to a left-continuous non-decreasing function g:[0,infinity)-> R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}xg '(t)is an element of F(t,x(t)),t is an element of[0,infinity)x(0)=x0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}we study the possibility to approximate the solutions of the convexified inclusion by the solutions of the non-convexified problem. Via a generalization to this framework of a classical result concerning continuous selection of trajectory, we thus present a relaxation theorem which states that, similarly to the setting of usual differential inclusions, the approximation can be achieved once we allow to the initial value to differ (but remaining close to) from the initial value of the considered solution of the relaxed inclusion
Vitali Theorems for Varying Measures
Full text linkThe classical Vitali theorem states that, under suitable assumptions, the limit of a sequence of integrals is equal to the integral of the limit functions. Here we
consider a Vitali type theorem of the following form
for a sequence of pair and we study its asymptotic properties. The results}
are presented for scalar, vector and multivalued sequences of -integrable functions .
The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense for Pettis and McShane integrability.
A list of known results on this topic is cited and new results are obtained when the ambient space is not compact
An equivalent definition of the vector-valued McShane integral by means of partitions of unity
Full text linkAn integral for vector-valued functions on a σ-finite outer regular quasi-radon measure space is defined by means of partitions of unity and it is shown that it is equivalent to the McShane integral. The multipliers for both the McShane and Pettis integrals are characterize
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