On a fixed-point theorem on locally convex linear topological spaces

Iff is a self mapping on a closed convex subsetK of a separated quasicomplete locally convex linear topological spaceE such that (i)E is strictly convex, (ii)f (K) is contained in a compact subset ofK and (iii)f satisfies a contraction condition, then it is shown that for eachxK, the sequence of {U ⁿ (x)} _n =1 of iterates, whereU KK is defined byU (y)=f(y)+(1-) y, yK, converges to a fixed point off.     

Deformation in locally convex topological linear spaces

We are concerned with a deformation theory in locally convex topological linear spaces. A special "nice" partition of unity is given. This enables us to construct certain vector fields which are locally Lipschitz continuous with respect to the locally convex topology. The existence, uniqueness and continuous dependence of flows associated to the vector fields are established. Deformations related to strongly indefinite functionals are then obtained. Finally, as applications, we prove some abstract critical point theorems.     

GENERALIZED BOCHNER THEOREM ON LOCALLY CONVEX SPACES

ThisworkissupportedinpartbythePostdoctoralScienceFoundationofChina.1.IntroductionTheclassicalBochnertheoremstatesthatafunctionCiR"-CisthecharacteristicfunctionofaprobabilitymeasureonR"iffCispositivedefinite,C(0)=1andcontinuous.FOrvariousgeneralizationsofthetheoremtoinfinitedimensionspaces,thereaderisreferredto{1]andT3I.Inthemonographl'],MinlostheoremgeneralizestheclassicalBochnertheoremtonuclearspaces,whichcharacterizestheclassofcharacteristicfunctionalsofRadonprobabilitymeasuresonstron…     

Diestel-Faires定理在局部凸空间中的推广

通过Banach 空间与局部凸空间的对比,将Banach 空间上的Diestel-Faires 定理在局部凸空间上进行推广。进一步给出了局部凸空间上的Orlicz-Pettis定理与推论。     

On an extension of Rolle's theorem to locally convex spaces

This work concerns the extension of a weak form of the Rolle's theorem to locally convex spaces that satisfy an axiom of separation. The result provides a condition for asserting the uniqueness of a solution to nonlinear functional equations, including nonlinear integro-differential equations. We use the extended Rolle's theorem to prove the uniqueness of a solution to a nonlinear, fractional differential equation.     

A class of generalised minimum effort problems in locally convex linear topological spaces

In this paper a class of generalised minimum effort problem has been formulated in locally convex linear topological spaces. Some necessary conditions has been obtained. Existence and uniqueness of the solutions are discussed     

Generalized quasi-variational inequalities in locally convex topological vector spaces

Let E be a Hausdorff topological vector space and X ? E an arbitrary nonempty set. Denote by E′ the dual space of E and the pairing between E′ and E by 〈w, x〉 for w?E′ and x?E. Given a point-to-set map S: X → 2^X and a point-to-set map T: X → 2^E′, the generalized quasi-variational inequality problem (GQVI) is to find a point $\text{y}\text{?}\text{? S(}\text{y}\text{?}\text{)}$ and a point $\text{u}\text{?}\text{? T(}\text{y}\text{?}\text{)}$ such that $\text{Re}\text{〈}\text{u}\text{?}\text{,}\text{y}\text{?}\text{? x〉 ? 0}$ for all $\text{x ? S(}\text{y}\text{?}\text{)}$. By using the Ky Fan minimax principle or its generalized version as a tool, some general theorems on solutions of the GQVI in locally convex Hausdorff topological vector spaces are obtained which include a fixed point theorem due to Ky Fan and I. L. Glicksberg, and two different multivalued versions of the Hartman-Stampacchia variational inequality.     

Basic sequences and non locally convex topological vector spaces

The paper is concerned with some application of basic sequences in the theory of non-locally convex topological vector spaces. Some results of Kalton, Peck, Gregory and Shapiro are extended.