Korovkin sets in locally convex function spaces

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

RESTRICTED p-CENTERS FOR SETS IN REAL LOCALLY CONVEX SPACES

Let X ,Z be a pair of real linear spaces put in duality by a separating bilinear form 〈, 〉, and endowed with compatible locally convex topologies respectively. A subset F of X is said to be p-bounded if sup p(x) : x ∈ F < ∞. We denote the collection of all nonempty p-bounded subsets of X by p(X ). Given x ∈ X , F ∈ p(X ), and V ⊆ X , write rp(F ; x) = sup p(y − x) : y ∈ F , radp(F ;V ) = inf rp...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

on the dual of certain locally convex function spaces

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

Some results on functionally convex sets in real Banach spaces

‎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...