the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...

In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilibrium constraint on metric spaces. We study these problems without any convexity and compactness assumptions. Our results are different from any existence results of these types of problems...

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems in finitely continuous topological spaces (in short, FC-spaces). By a maximal element theorem in product FC-spaces, we prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. These theorems improve, unify many important result in recent li...

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...

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

In this paper, the author considers generalized minimax theorems for vector set-valued mappings using Fan-KKM theorem on nonconvex domains of Hausdorff topological vector spaces.

For a new class of topological vector spaces, namely κ-normed spaces, an associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κ-norm, that is a distance function between a point and a G δ-subset. For it, analogs of the Hahn-Banach theorem are proved.