Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...

We discuss the concept of the bisector of a segment in a Minkowski normed n-space. We prove that all bisectors are topological images of a plane of the embedding Euclidean 3-space iff the shadow boundaries of the unit ball K are topological circles. To a conjectured proving strategy for dimensions n, we introduce the concept of general parameter sphere of the unit ballK, corresponding to a dire...

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](G), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L(2) Fourier transform, when restricted to functions in...

Bogdan and Kolumbán [3] gave sufficient conditions for closedness of the solution map defined on the set of parameters. They considered the parametric equilibrium problems governed by topological pseudomonotone maps depending on a parameter. In this paper we generalize this result for parametric vector equilibrium problems with trifunctions. Let X and Y be Hausdorff topological spaces and P , t...

In this paper,we consider a parametric generalized vector quasiequilibriumproblemwhich is mixed in the sense that several different relations can simultaneously appear in this problem. The moving cones and other data of the problem are assumed to be set-valued maps defined in topological spaces and taking values in topological spaces or topological vector spaces. The main result of this paper g...

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of variational inequalities.

In this paper, the solvability of a class of strong vector quasi-equilibrium problems(for short, SVQEP) are studied in real topological vector space. By using the Kakutani-Fan-Glicksberg fixed point theorem, some existence theorems for SVQEP are obtained without any monotonicity assumption.

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...