In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

Existence theorems of generalized variational inequalities and generalized complementarity problems are obtained in topological vector spaces for demi operators which are upper hemicontinuous along line segments in a convex set X . Fixed point theorems are also given in Hilbert spaces for set-valued operators T which are upper hemicontinuous along line segments in X such that I − T are demi ope...

Preface In the notion of a topological vector space, there is a very nice interplay between the algebraic structure of a vector space and a topology on the space, basically so that the vector space operations are continuous mappings. There are also plenty of examples, involving spaces of functions on various domains, perhaps with additional properties, and so on. Here we shall try to give an in...

where f is a continuous function of compact support onGwith values in V . This is not quite a trivial matter. If V is assumed to be complete, a definition by Riemann sums works quite well, but this is an unnecessarily strong requirement. The natural condition on V seems to be that it be quasi-complete, a somewhat technical but nonetheless valuable condition. Continuous representations of a loca...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...