In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equival...In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.展开更多
Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. I...Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. In this work we will be concerned with the relationship between bounded operators , and X-valued integrals on . When X is a Banach space, such relation has been completely achieved via Bochner integral in [1]. In this paper we investigate the context of locally convex spaces and we will focus attention on weak integrals, namely the Pettis integrals. Some results in this direction have been obtained, under some special conditions on the structure of X and its topological dual X*. In this work we consider the case of a semi reflexive locally convex space and prove that each Pettis integral with respect to a signed measure μ, on S gives rise to a unique bounded operator , which has the given Pettis integral form.展开更多
This article studies some convergence results for the McShane integral of functions mapping the interval [0, 1] into a Banach space X from the point of view of an open problem proposed by D.H.Fremlin and J. Mendoza in...This article studies some convergence results for the McShane integral of functions mapping the interval [0, 1] into a Banach space X from the point of view of an open problem proposed by D.H.Fremlin and J. Mendoza in [2], also the authors give a negative answer to this open problem.展开更多
In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E）...In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.展开更多
Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a n...Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence展开更多
Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bil...Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.展开更多
文摘In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.
文摘Let X be a topological vector space and let S be a locally compact space. Let us consider the function space of all continuous functions , vanishing outside a compact set of S, equipped with an appropriate topology. In this work we will be concerned with the relationship between bounded operators , and X-valued integrals on . When X is a Banach space, such relation has been completely achieved via Bochner integral in [1]. In this paper we investigate the context of locally convex spaces and we will focus attention on weak integrals, namely the Pettis integrals. Some results in this direction have been obtained, under some special conditions on the structure of X and its topological dual X*. In this work we consider the case of a semi reflexive locally convex space and prove that each Pettis integral with respect to a signed measure μ, on S gives rise to a unique bounded operator , which has the given Pettis integral form.
基金Supported by NNSF of China(10571085)Science Foundation of Hohai University and grant No.201/04/0690 of the GA of the Czech Republic
文摘This article studies some convergence results for the McShane integral of functions mapping the interval [0, 1] into a Banach space X from the point of view of an open problem proposed by D.H.Fremlin and J. Mendoza in [2], also the authors give a negative answer to this open problem.
文摘In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.
基金Supported by the Polish Ministry of Science and Higher Education(Grant Nos.N N201 414939 for M.Balcerzak,N N201 416139 for K.Musial)
文摘Let （Ω,∑,μ） be a complete probability space and let X be a Banach space. We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem. We Mso obtain a Vituli type Z-convergence theorem for Pettis integrals where Z is an ideal on N. Keywords Convergence theorems for integrals, Pettis integral, scalar equi-convergence in measure, Z-convergence
文摘Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.
