Mappings In Topological Vector Spaces Research Articles

New matching theorems for admissible type maps in topological vector spaces

New matching theorems for admissible type maps in topological vector spaces

Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces

This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.

On generalized implicit vector variational inequality problems

In this paper, we introduce and study the generalized implicit vector variational inequality problems with set valued mappings in topological vector spaces. We establish existence theorems for the solution set of these problems be nonempty compact and convex. Our results extend the results by Fang and Huang [ Existence results for generalized implicit vector variational inequalities with multivalued mappings, Indian J. Pure and Appl. Math. 36(2005), 629–640.]

Existence of Solutions to Generalized Vector Variational-Like Inequalities

This paper deals with some existence theorems for generalized vector variational-like inequalities with set-valued mappings in topological vector spaces. The results presented in this paper generalize and improve some previously known results in the literature.

On Generalized Vector Equilibrium Problems

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi-concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established.

Transfer positive hemicontinuity and zeros, coincidences, and fixed points of maps in topological vector spaces

Let be a real Hausdorff topological vector space. In the present paper, the concepts of the transfer positive hemicontinuity and strictly transfer positive hemicontinuity of set-valued maps in are introduced (condition of strictly transfer positive hemicontinuity is stronger than that of transfer positive hemicontinuity) and for maps and defined on a nonempty compact convex subset of , we describe how some ideas of K. Fan have been used to prove several new, and rather general, conditions (in which transfer positive hemicontinuity plays an important role) that a single-valued map has a zero, and, at the same time, we give various characterizations of the class of those pairs and maps that possess coincidences and fixed points, respectively. Transfer positive hemicontinuity and strictly transfer positive hemicontinuity generalize the famous Fan upper demicontinuity which generalizes upper semicontinuity. Furthermore, a new type of continuity defined here essentially generalizes upper hemicontinuity (the condition of upper demicontinuity is stronger than the upper hemicontinuity). Comparison of transfer positive hemicontinuity and strictly transfer positive hemicontinuity with upper demicontinuity and upper hemicontinuity and relevant connections of the results presented in this paper with those given in earlier works are also considered. Examples and remarks show a fundamental difference between our results and the well-known ones.

Fixed points of condensing multivalued maps in topological vector spaces

With the aid of the simplicial approximation property, we show that every admissible multivalued map from a compact convex subset of a complete metric linear space into itself has a fixed point. From this fact we deduce the fixed point property of a closed convex set with respect to pseudocondensing admissible maps.

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasiconvex mappings in topological vector spaces is defined, and their fundamental properties are presented. The relationships between the cone bounded quasiconvex mapping defined in this paper and cone convex mapping, and other known cone quasiconvex mapping are also discussed.

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces

Fixed point theory and generalized Leray-Schauder alternatives for approximable maps in topological vector spaces

Some new fixed point theorems for approximable maps are obtained in this paper. Homotopy results, via essential maps, are also presented for approximable maps.

Fixed point theorems for condensing admissible maps in topological vector spaces

Introducing the notion of c-measure of noncompactness due to S. Hahn, we give a homotopy extension theorem and the fixed point property for pseudo-condensing admissible maps in general topological vector spaces. Moreover, these results are applied to obtain a Leray-Schauder type fixed point theorem for pseudo-condensing admissible maps in topological vector spaces which includes many known results.

A Leray–Schauder type theorem for approximable maps in topological vector spaces

A Leray–Schauder type theorem for approximable maps in topological vector spaces

Fixed points for convex continuous mappings in topological vector spaces

We prove the following result. Let $C$ be a convex compact subset in a topological vector space, and $T:C\to C$ a convex continuous mapping. (See Definition 1.1.) Then $T$ has a fixed point. Moreover, continuous mappings that can be approximated by convex continuous mappings also have the fixed point property.

Loose saddle points of set-valued maps in topological vector spaces

We give a new existence theorem for loose saddle point of set-valued map having values in a partially ordered topological vector space which is based on continuity and quasiconvexity- quasiconcavity of its scalarized maps. Moreover, we prove a new saddle point theorem for vector-valued functions in locally convex topological vector spaces under weak condition that is the semicontinuity of two function scalarization.

Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps

This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained

Fixed point and coincidence theorems of set-valued mappings in topological vector spaces with some applications

Fixed point and coincidence theorems of set-valued mappings in topological vector spaces with some applications

Some fixed point and almost fixed point theorems for multivalued mappings in topological vector spaces

Some fixed point and almost fixed point theorems for multivalued mappings in topological vector spaces

A fixed point theorem for multivalued mappings in topological vector spaces

A fixed point theorem for multivalued mappings in topological vector spaces

On extending and lifting continuous linear mappings in topological vector spaces

On extending and lifting continuous linear mappings in topological vector spaces

On extension of continuity and application of countability axioms in topological tensor products

In this paper an attempt has been made to prove an analogue of the result1 on the extension of linear and continuous mappings in topological vector spaces to the context of topological tensor products.