We continue our study on Massera type theorems in hyperfunctions from [11] and [12]. In the latter, we gave a result in hyperfunctions with values in a reflexive Banach space. In this article, we report its generalization to the case of hyperfunctions with values in a reflexive locally convex space. AMS Mathematics Subject Classification (2010): Primary 32A45; Secondary 32K13

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Let Γ = (P,L) be a parapolar space which is locally An−1,3(K) for some integer n > 6 and K a field. There exists a class of 2-convex subspaces D, each isomorphic to D5,5(K), such that every symplecton of Γ is contained in a unique element of D. Let Γ = (P,L) be a parapolar space which is locally An−1,4(K) for n = 7 or an integer n ≥ 9 and some field K. Assume that Γ satisfies the extra conditio...

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space. 1. Problem statement Let (X , ‖ · ‖) be a reflexive real Banach space with dual (X ∗, ‖ · ‖∗) and let f : X → ]−∞,+∞] be a lower semicontinuous (l.s.c.) convex function which is Gâteaux differentiable on int dom f 6= Ø and Legendre [1, D...

The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...