As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, decomposable and as well their corresponding hull operators acting on power sets Lebesgue-Bochner spaces. We show that coincides in finite-dimensional setting, yet tends to be larger infinite dimensions. also provide a quantitative characterization hull, without an...

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the uni…cation and re…nement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years ...

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

We characterize the local single-valuedness and continuity of multifunctions (set-valued mappings) in terms of their submonotonicity and lower semicontinuity. This result completes the well-known condition that lower semicontinuous, monotone multifunctions are single-valued and continuous. We also show that a multifunction is actually a Lipschitz single-valued mapping if and only if it is submo...

Kamae, et. al. [8, Theorem 1] presents a general characterization of the partial ordering of probability measures induced by a closed partial ordering on the underlying Polish state space. A preorder is a reflexive and transitive, but not necessarily antisymetric relation. This paper presents a similar characterization of the preordering of probability measures induced by a measurable preorderi...

Necessary conditions of optimality are derived for optimal control problems with pathwise state constraints, in which the dynamic constraint is modelled as a differential inclusion. The novel feature of the conditions is the unrestrictive nature of the hypotheses under which these conditions are shown to be valid. An Euler Lagrange type condition is obtained for problems where the multifunction...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

Relying on the continuous approximate selection method of Cellina, ideas and techniques from Sobolev spaces can be applied to the theory of multifunctions and differential inclusions. The first part of this paper introduces a concept of graph completion, which extends the earlier construction in [10] to functions of several space variables. The second part introduces the notion of Cellina W 1,p...

We prove the existence of strong solutions to a nonlinear evolution equation of the form  u′(t) + g(t) = f(t) + h(t) g ∈ SL2{∂φ(u(·))} f ∈ SL2{F (·, u(·))} u(0) = −u(T ), in a Hilbert space H, where φ : D(∂φ) ⊂ H → IR+ is a proper, convex, l.s.c. function of compact type, F : [ 0, T ]×D(∂φ)→ 2 is a multifunction which is demiclosed and dominated in some sense by ∂φ and h ∈ L(0, T ;H) is suf...