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 ...

We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Dane s' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto eeciency theorem due to Isac. Concerning the drop theorem this solves a problem proposed by G. Isac in 1997. We show that another formulation ...

0.1. Analytic vectors and their analytic continuation. Let G be a Lie group and (π,G, V ) a continuous representation of G in a topological vector space V . A vector v ∈ V is called analytic if the function ξv : g 7→ π(g)v is a real analytic function on G with values in V . This means that there exists a neighborhood U of G in its complexification GC such that ξv extends to a holomorphic functi...

The goal of this paper is to find the "Lie groups" for three well-known Lie algebras: the globally Hamiltonian vector fields, the infinitesimal quantomorphisms and the homogeneous real-valued functions of degree one on the cotangent bundle minus the zero section. In all our considerations the underlying manifold is assumed to be compact without boundary. Before explaining and motivating our res...

Formally, distributions are usually defined as continuous linear functions on a certain topological vector space of “test functions”. However, it is not surprising that useful mathematical objects such as distributions also have a natural, concrete description. We shall start from this viewpoint, and later explain the abstraction to topological vector spaces, and explain why the latter is impor...

An elementary geometric construction is used to relate the space of lattices in R to the space exp3 S 1 of the subsets of a circle of cardinality at most 3. As a consequence we obtain a new proof of known statements about the space exp3 S . Spaces of finite subsets. For X a topological space let exp k X be the set of all finite subsets of X of cardinality at most k. There is a map from the Cart...

This study considers four means of defining differential operators for extracting local aspects of shape in ill-specified environments: fuzzy differentiation as kernel smoothing; differentiation in the sense of weak or generalized derivatives; differentiation for fuzzy functions between normed spaces; and fuzzy differentiation for mappings between fuzzy manifolds. More consideration is given to...

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R θ ×S2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S, we reduce the Donaldson-Uhlenbeck-Yau equations on R θ ×S2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R θ . In the SO(3)-invariant...